Upon the king being told there was a secret message for him to be told in silence, why would the translation have the king instead say "Silence!" and the people know to just leave? Wouldn't they have to be told by the king to leave first so that the secret message could be told in privacy?
But he himself turned back from the idols which were at Gilgal, and said, “I have a secret message for you, O king.” And the king said, “Silence!” And all who were attending him left him.
The king said just one word הָ֔ס . It is an interjection, apparently based on an imperative based on the verb הסה , meaning to be silent. Even the Jewish Publication Society translates it this way:
But he himself returned from Pesilim, near Gilgal, and said, “Your Majesty, I have a secret message for you.” [Eglon] thereupon commanded, “Silence!” So all those in attendance left his presence; ... (Judges 3:19, JPS1985)
Lexicons
הַס : interj., English hush; Schulthess Zurufe 20, 64; Arb. hus; Tigr. Wb. 13a hes: הָֽס, pl. (as pi. impv., BL 652b; VG 1:503) הַסּוּ Neh 8:11: hush! keep silence! order to keep sacred silence (favēte linguis!) Ju 3:19 Am 6:10 Neh 8:11, הַס מִפְּנֵי י׳ Zeph 1:7 Zech 2:17, מִפָּנָיו כָּל־הָאָרֶץ Hab 2:20 at the offering ?; —? Am 8:3, → Comm. † Der. הסה.
הסה: denom. from הַס; MHb.2 to be silent (?), ולא להס it cannot be kept silent (alt.: should not become silent) 1QH 10:15; Arb. hassa to whisper, hashasat secretive talk (Schulthess ZS 2:15f). hif: impf. וַיַּ֫הַס (Bergsträsser 2:164k, c) to quieten the people (with אֶל for) Nu 13:30. † -- Koehler, L., Baumgartner, W., Richardson, M. E. J., & Stamm, J. J. (1994–2000). In The Hebrew and Aramaic lexicon of the Old Testament (electronic ed., p. 253). E.J. Brill.
†הַס S2013 TWOT511 GK2187, הָ֑ס interj. hush! keep silence (prob. onomatop.) Ju 3:19 and he said, I have a secret errand unto thee, O king, וַיֹּאמֶר הָ֔ס and he said, Keep silence! Am 6:10 וְאָמַר הָ֔ס (while burying men in a pestilence), 8:3 (ellipt.) in every place הִשְׁלִיךְ הָֽס׃ they cast them (the corpses) forth, (saying) Hush! sq. (מִפָּנָיו) מִפְּנֵי י׳ Hb 2:20 Zp 1:7 Zc 2:17. Inflected, as though a verb, imv. pl. הַ֔סּוּ Ne 8:11 (Ges compares Arabic هَلُمَّ (halumma) [ = הֲלֹם] hither! inflected as an imv., e.g. هَلُمِّى, هَلُمُّوا (halummī, halummū): W i. § 368). Hence as denom. †Hiph. impf. apoc. וַיַּ֫הַס Nu 13:30 and Caleb stilled the people. -- Brown, F., Driver, S. R., & Briggs, C. A. (1977). In Enhanced Brown-Driver-Briggs Hebrew and English Lexicon (p. 245). Clarendon Press.
