Save "Keshet true and false"
Keshet true and false
וַיִּסֹּ֣גוּ וַֽ֭יִּבְגְּדוּ כַּאֲבוֹתָ֑ם נֶ֝הְפְּכ֗וּ כְּקֶ֣שֶׁת רְמִיָּֽה׃

They fell away, disloyal like their fathers;
they played false like a treacherous bow.

-- JPS 1985

but turned back, and dealt unfaithfully like their fathers: they were turned aside like a deceitful bow. -- Koren

And they backslid and were as traitorous as their fathers. They turned [(from one direction to another)] as a deceiving bow [(which always misses the target)].

-- RASHI Ketuvim (Silverstein)

כקשת רמיה. שאינה זורקת חץ למקום שהמורה חפץ:
like a deceitful bow which does not shoot the arrow to the place the archer wishes.
Robert Alter translates:
"They fell back and betrayed like their fathers, whipped around like an untrusty bow."
He adds this note:
"The image seems to be of a bow that flips out of the hands of the archer, shooting the arrow in the wrong direction, or not shooting at all."
from The Jerusalem Commentary on the Psalms. Mosad Harav Kook, 2003
They turned around and walked in the opposite direction to God's path, like a deceitful bow that deceives the archer, for he aims to fire arrows to the east, and the arrows fly off to the west. In the same way, God commanded the people of Israel to keep His law but the did the opposite...The words k'keshet r'miyyah, "like a deceitful bow," may possibly be hinting at the common expression l'shon r'miyyah, "a deceitful tongue" (see Jeremiah 9:7: "Their tongue is a sharpened arrow, it speaks deceit"). The psalmist is suggesting that the people swore with their tongues to keep God's commandments but they did the opposite.

...

אמר לשונך דומה לתער מלוטש אשר יגלח בו האדם. יעשה התער רמיה. ובמקום שיחתוך השער לבד, יחתוך גם הבשר עמו. והוא משל [מבוקש] לענין דואג. שֶׁדִּבֶר טוב על לב המלך שאול, כמרחם עליו להסיר דאבון לבו, ובדבריו אלה השחית בית אחימלך. ואל תתמה על מלת "רמיה" שיהיה תאר לתער, כי דוגמתו "נהפכו כקשת רמיה" (תהלים עח, נז). כי מלת "רמיה" נופלת גם על דבר שאין בו רוח חיים. ופירוש זה מתוקן. עתה ראיתי לרש"י ז"ל "עושה רמיה, חותך הבשר עם השֵׂעָר", ע"כ. ויפה פירש ותבין דבריו ממה שדברנו.

on RAMIAH

Gan Naul (~1765) is listed on Sefaria as "One of the first modern studies of Hebrew language and grammar." Sefaria does not have a translation for this (yet), but I share it because I hadn't run into this particular reference before and thought it interesting.

The passage excerpted here comes up as commentary on Psalm 78:57. It focuses on the word "ramiah," and, like Jerusalem Commentary (cited above) highlights "deceitful tongue" as a "common expression" I can make out emphasis on tongues and words, plus Doeg, an adviser of King Saul and an exemplar of deceit in midrash.

That's all I can get myself without a lot more effort.

Doeg, the Edomite, a trusted adviser of King Saul
According to aggadah, among the reasons he was called the Edomite (the red) were: his superior Torah learning enabled him to redden the faces of those shamed at their ignorance; his jealousy and hatred of David...; his permitting the bloodbath at the priestly city of Nob in revenge for its sheltering David when he fled from Saul; his attempt to refute the legitimacy of David as a descendant of Ruth the Moabite; and his causing Saul to sin by failing to shed the blood of Agag in direct disobedience of a Divine command (Mid. Ps. 52:4)
Doeg had a passion for evil speech....
-- Ronald L. Eisenberg, Essential Figures in the Bible. Jason Aronson 2013, p.51
---- so happy to have a reason to make use of this book, which I bought by mistake!
יָשׁ֣וּבוּ ׀ לֹ֣א עָ֗ל הָיוּ֙ כְּקֶ֣שֶׁת רְמִיָּ֔ה יִפְּל֥וּ בַחֶ֛רֶב שָׂרֵיהֶ֖ם מִזַּ֣עַם לְשׁוֹנָ֑ם ז֥וֹ לַעְגָּ֖ם בְּאֶ֥רֶץ מִצְרָֽיִם׃

They come back;
They have been of no use,
Like a slack bow.
Their officers shall fall by the sword,
Because of the stammering of their tongues.
Such shall be [the results of] their jabbering
In the land of Egypt. -- JPS 1985

They turn to them, but to no avail: they are like a deceitful bow... -- Koren Translation

היו כקשת רמיה. כשרוצה לירות בו חץ לצפון הוא יורה לדרום:
they were like a deceitful bow which, when one wishes to shoot with it toward the north, shoots toward the south.
Full DICTIONARY ENTRIES for Keshet and Ramiah
BDB for KESHET
קֶ֫שֶׁת n.f. Gn 9:14 (appar. m. 2 S 1:22 but v. AlbrZAW xvi (1896) 91) bow (orig. √ perhaps קושׁ, meaning unknown; NH id.; Assyrian ḳaštu; Ethiopic ቀስት: Arabic قَوْسٌ, pl. قُسِىٌّ, قِسِىٌّ, etc.; 𝔗 קַשְׁתָּא and (ט for ת after ק) קוּשְׁטָא (rare), all bow, קַשָּׁתָא bowman; Syriac ܩܶܫܬܳܐ bow, ܩܰܫܳܬܳܐ bowman; Old Aramaic קשת bow, Mand. כשטא (Frä 206); Palm. קשטא bowman);—abs. ק׳ Ho 1:7 +, קָ֑שֶׁת Je 46:9 +; cstr. קֶ֫שֶׁת Ho 1:5 +; sf. קַשְׁתִּי Gn 48:22 +, etc.; pl. abs. קְשָׁתוֹת 2 Ch 26:14 +; sf. קַשְּׁתֹתָיו (Ges§ 20 h) Is 5:28, קַשְּׁתוֹתָם Je 51:56 ψ 37:15, קַשְּׁתֹתֵיהֶם Ne 4:7 (קַשְׁתֹּתָיו etc., van d. H. [except ψ 37:15]);—

1. bow: a. for hunting Gn 27:3 (J; + תְּלִי). b. battle: + (or ‖) חֶרֶב, Gn 48:22; Jos 24:12 (both E), Ho 1:7; 2:20 1 S 18:4 (+ חֲגֹרוֹ), 2 S 1:22; 2 K 6:22; Is 41:2 Ne 4:7 (+ רָמְחֵיחֶם), Zc 9:13 (fig. of Judah as י׳’s bow), ψ 37:15 (fig.), 44:7 (+ or ‖ חֶרֶב also infr.); + (or ‖) חִזִּים Is 7:24; 2 K 13:15(×2); Ez 39:3, 9; 1 Ch 12:2a; cf. רִשְׁפֵי ק׳ ψ 76:4 = arrow (+ מָגֵן וְחֶרֶב) so בֶּן ק׳ Jb 41:20 (cf. La 3:13; Jb 5:7); + חֲנִית ψ 46:10, + כִּידוֹן Je 6:23; 50:42; + various weapons Ne 4:10; 2 Ch 26:14; alone Is 13:18 (context corrupt), 22:3; Je 51:56; Hb 3:9 (of י׳ as warrior); ק׳ מִלְחָמָה Zc 9:10; 10:4; in sim. כְּק׳ רְמִיָּה like a bow of deception Ho 7:16 ψ 78:57 (i.e. one that misses its aim; al. slack bow). c. ק׳ coll. = bow(-men), archers Is 21:17. d. phrases are: הַמּוֹרִים אֲנָשִׁים בַּקּ׳ 1 S 31:3 archers, bowmen (but dub.; Dr Kit Löhr tr., א׳ הַמּ׳; We Bu del. א׳, as ‖ 1 Ch 10:3; HPS Now del. א׳ בַּקּ׳), הַמּוֹרִים בַּקּ׳ 1 Ch 10:3; מְטַחֲוֵי ק׳ Gn 21:16 (v. [טָחָה]), רמֵה ק׳ Je 4:29, cf. perhaps Gn 21:21 v. קַשַּׁת, ‖ נשְׁקֵי ק׳ (v. II. נָשַׁק) 1 Ch 12:2 b; 2 Ch 17:17, נוֹ׳ רוֹמֵי ק׳ ψ 78:9; תֹּפֵשׂ הַקּ׳ Am 2:15 one grasping the bow, (v. Je 46:9 infr.) v. also מִלֵּא יָדוֹ בַקּ׳ 2 K 9:24, הַרְכֵּב יָֽדְךָ עַל־הַקּ׳ 13:16; דָּרַךְ ק׳ bend (lit. tread) the bow, Is 5:28 (pt. pass), 21:15 (id.;חֶרֶב), Je 50:14, 29; 51:3; 1 Ch 5:18; 8:40; 2 Ch 14:7; ψ 37:14 (‖ חֶרֶב), in fig. 11:2 (‖ חֵץ), and, of God, La 2:4; 3:12 ψ 7:13 (‖ חֶרֶב); תֹּפְשֵׂי דֹּרְכֵי ק׳ Je 46:9; cf. (fig.) וַיַּדְרְכוּ אֶת־לְשׁוֹנָם קַשְׁתָּם Je 9:2; also וְנִחֲתָה ק׳ נְחוּשָׁה ψ 18:35 = 2 S 22:35 (read וְנִחֲתָה for וְנִחַת); מָשַׁךְ בַּקּ׳ draw the bow 1 K 22:34 = 2 Ch 18:33; Is 66:19. e. bow (passing over into) fig. of might, Gn 49:24 (poem), 1 S 2:4; Ho 1:5; Je 49:35; Jb 29:20 (cf. ψ 37:15, b. supr.). f. ק׳ נְחוּשָׁה fig. of divine judgment Jb 20:24 (‖ נֵשֶׁק בַּרְזֶל).

2. rainbow: כְּמַרְאֵה הַקּ׳ אֲשֶׁר יִהְיֶה בֶעָנָן בְּיוֹם הַגֶּשֶׁם Ez 1:28; Gn 9:13, 14, 16 (P).—וַיֹּאמֶד לְלַמֵּד בְּנֵי־יְהוּדָה קָ֑שֶׁת 2 S 1:18 is corrupt; 𝔊 al. om.; We Now think misplaced gloss on v 6; v. further HPS.
Jastrow for KESHET (b.h.) -- קֶשֶׁת
construct form (b. h.; [VERB BELOW]) bow; rainbow. Erub. 55ᵃ עיר העשויה כק׳ a town built in the shape of a bow; ib. עשויה כמין ק׳. Ber. 59ᵃ הרואה את הק׳ בענן he who sees a rainbow in the clouds. Ḥag. 16ᵃ. Gen. R. s. 35; a. fr.—Pl. קְשָתוֹת. Lam. R. introd. (R. Joḥ. 1) (ref. to Is. XXII, 3) שהיו מתירין גידי קַשְׁתּוֹתָם וכ׳ they loosened the strings of their bows and tied them with them; Yalk. Is. 289. Sifré Deut. 18 עקרבים כק׳ scorpions as large as bows; Yalk. ib. 803; a. e.—Trnsf. membrum virile, potentia virilis. Sot. 36ᵇ; Y. Hor. II, 46ᵈ; a. e.
VERB FORM
קְשַׁת, קְשֵׁית
(v. קְשַׁט) to shoot. Targ. Ez. XXI, 26. Targ. Y. II, Ex. XV, 4; a. e.
Af. - אַקְשֵׁית same. Targ. Is. XXXVII, 33 יַקְשִׁית ed. Wil. (ed. Lag. יִקְשַׁת); Targ. II Kings XIX, 32.
Ithpa. - אִתְקַשֵּׁת to be shot forth. Targ. Y. II, Ex. XIX, 13 (v. קְשַׁט).
Kashat [with a tet] "see also" citation from k'shat/k'sheit (above) Biblical Hebrew --- קְשַׁט
m. (b. h.) [to be straight, strong,] 1) to go in a straight line, to shoot forth. Num. R. s. 12 יש מזיק … וקוֹשֵׁט כחץ some demon flies like a bird and shoots through the air like an arrow; Midr. Till. to Ps. XCI; Yalk. ib. 842 וקוֹשֵׁת; Tanḥ. Naso 23 וקושש (corr. acc.); ed. Bub. 28.—Y. Meg. I, 72ᵇ מאיכן ק׳ הקוֹשֵׁט הזה וכ׳ whence did this archer shoot (whence did he derive the opinion) that &c. (cmp. יָרָה Hif.). —2) to correct. B. Mets. 107ᵇ, v. infra.
Pi. - קִישֵּׁט 1) to shoot, aim, direct. Tosef. Erub. IX (VI), 26 ביבין המְקַשְּׁטִין וכ׳ ed. Zuck. (Var. המשקטין, המְקַשְׁקְשִׁין, v. קִשְׁקֵשׁ II) gutters which gush under the houses (cmp. קָלַח). Lam. R. to III, 12 מקושטים בה Ar. s. v. קורה, read: מְקַשְּׁטִים (Ar. ed. Koh. מְקוֹשְׁשִׁים; ed. מוֹרִים), v. חֵץ.—Part. pass. מְקוּשָּׁט; f. מְקוּשֶּׁטֶת; pl. מְקוּשָּׁטִים, מְקוּשָּׁטִין; מְקוּשָּׁטוֹת. Pesik. R. s. 40 (play on מוריה, with ref. to ירה יירה, Ex. XIX, 13) שהיתה מק׳ כנגד וכ׳ it (the holy land) was aimed towards (directly under) the heavenly altar (v. כּוּן); Yalk. Cant. 988. Ib. כשם שגודלת הזו … להיות מקושטים וכ׳ (not מקושטת) as the hair-dresser dressing the bride puts every ornament in its proper place, so must the words of the Law be aimed, every word in its due place. —2) (cmp. תקן) to dress, adorn, prepare. Ib. שמְקַשֶּׁטֶת לכלה, v. supra. Gen. R. s. 8 מְקַשֵּׁט כלות he (the Lord) attires brides; Koh. R. to VII, 2. Ib.; Gen. R. s. 18 משקִשְּׁטָהּ וכ׳ after having fitted her out with twenty-four kinds of ornaments; a. fr.—Part. pass. as ab. Sabb. 25ᵇ מטה מוצעת ואשה מק׳ לתלמיד חכם the scholar’s happiness when the couch is spread and the wife dressed (for the Sabbath). Ib. 153ᵃ כשהן מק׳ in festive dress, opp. מלוכלכין; a. fr.—Trnsf. to set right, correct. Snh. 18ᵃ (ref. to התקוששו וקושו, Zeph. II, 1) קַשֵּׁט … קשט אחרים first correct thyself, then correct others; ib. 19ᵃ; B. Bath. 60ᵇ; B. Mets. 107ᵇ קְשׁוֹט וכ׳; Yalk. Jer. 302; Midr. Till. to Ps. LIII אם תרצה לקַשֵּׁט אחרים וכ׳ if thou wishest to correct others, correct thyself first.
Hif. - הִקְשִׁיט to prepare, make ready. Gen. R. s. 28 הקב"ה היפך … והִקְשִׁיטָן וכ׳ the Lord turned day into night and prepared them for visitations; (Yalk. Job 920 והתקינן).
Hithpa. - הִתְקַשֵּׁט 1) to dress, adorn one’s self. Num. R. s. 2 אבן יקרה שמִתְקַשְּׁטוֹת וכ׳ a precious stone with which women adorn themselves; a. e. —2) to be verified, justified (cmp. קְשׁוֹט). Gen. R. s. 55 בשביל שתִּתְקַשֵּׁט וכ׳, v. קוֹשֶׁט; Yalk. ib. 95; Yalk. Ps. 777.
Kashat [with a tet] "see also" citation from k'shat/k'sheit (above) Aramaic
Pa. קַשֵּׁט 1) to straighten, correct. Targ. I Chr. XXIX, 18. —2) to go in a straight line, to shoot forth. Targ. Hos. VI, 3 מְקַשֵּׁיט (not מִ׳; ed. Lag. מקשט; h. text נכון). —3) to prepare. Yeb. 63ᵇ (of a bad wife) מְקַשְּׁטָא … ומקשטא וכ׳ has a tray ready for him, and has her mouth ready for him (to scold); מק׳ … ומחדרא וכ׳ prepares a tray for him, and turns her back to him.
Ithpa. - אִתְקַשֵּׁט, אִיקַּשַּׁט 1) to be shot. Targ. Y. II, Ex. XIX, 13 (ed. Vien. יתקשתין). —2) to be dressed, prepared. Targ. Is. LXI, 10. Targ. Am. IV, 12 (h. text הכין).—Taan. 23ᵇ כי מִיקַּשְּׁטָא is well dressed; a. e.
KESHET/KASHTA (Aramaic)
קֶשֶׁת, קַשְׁתָּא
1) bow; rainbow. Targ. Is. XXI, 15. Targ. Gen. XXI, 16. Ib. IX, 13; a. fr.—Pl. קַשְׁתִּין, קַשְׁתָּן, קַשְׁתָּתָא, קַשְׁוָותָא. Targ. Is. VII, 24. Targ. II Chr. XXVI, 14. Targ. I Sam. II, 4 קַשְׁתַּת constr. (followed by ד־). Targ. Y. Gen. XXI, 20. Targ. Ps. XXXVII, 14, sq.; a. e.
2) the curved side of the stomach, opp. to יִתְרָא. Ḥull. 50ᵃ דאק׳ the fat covering the curved &c.
BDB for RAMIAH
† I. רְמִיָּה n.f. deceit, treachery;—always abs. ר׳;—deceit, treachery: especially of speech, pred. of לָשׁוֹן Mi 6:12 (‖ שֶׁקֶר), appos. of לָשׁוֹן (or read לְשֹׁוֹן?) ψ 120:2 (‖ שְׂפַת שֶׁקֶר), v 3; of man, עֹשֵׂה ר׳ 52:4 that workest treachery, 101:7 (‖ דֹּבֵר שְׁקָרִים); also Jb 13:7; 27:4 (both ‖ עַוְלָה); deception ψ 32:2 (‖ עָוֹן); in phr. קֶשֶׁת ר׳ treacherous bow (sim.) Ho 7:16 ψ 78:57 (failing him who trusts to it).
Jastrow for RAMIAH

רמי, רָמָה

(b. h.) [to move,] to throw, swing. Mekh. B’shall., Shir., s. 2 (ref. to Ex. XV, 1 a. 4) ר׳ שהיו עולין למרום וכ׳ ramah means that they were hurled upward, yarah, that they were thrown down the deep.
Pi. - רִמָּה to impose upon, deceive; to be cunning. Y. Hor. III, 48ᵃ bot. (he was no deceiver) אלא שהיה מְרַמֶּה במצות but he was cunning in charitable deeds (waited until others had subscribed, and then gave as much as all of them combined); Deut. R. s. 4; Tanḥ. R’eh 5. Gen. R. s. 85 אתה רִמִּיתָ באביך בגדי … שתמר מְרַמָּה בך וכ׳ thou (Judah) didst deceive thy father by means of a kid (Gen. XXXVII, 31); by thy life! Tamar shall deceive thee through a kid (ib. XXXVIII, 20); Yalk. ib. 145 לאביך … לך; a. e.—Part. pass. מְרוּמֶּה. Snh. 32ᵇ, a. e. דין מ׳, v. דִּין II