Akademik

З-155
ДАВАТЬ/ДАТЬ (ПОДАВАТЬ/ПОДАТЬ obs) ЗНАК (кому) VP subj: human to make s.o. aware of sth. , use a signal to warn s.o. : X подал знак Y-y = X gave Y the (a) signal (sign) (to do sth. ) X signaled (to) Y (to do sth. ) (in refer, to signaling with one's eyes) X gave Y the eye.
Когда же (Митя) рассказал, как он решился наконец дать отцу знак, что пришла Грушенька и чтобы тот отворил окно, то прокурор и следователь совсем не обратили внимание на слово «знак», как бы не поняв вовсе, какое значение имеет тут это слово... (Достоевский 1). When he (Mitya) told how he finally made up his mind to give his father the signal that Grushenka had come, so that he would open the window, the prosecutor and the district attorney paid no attention to the word "signal," as if they had no idea at all of the word's significance here... (1a).
...(Император) подал рукою знак. Раздался одинокий выстрел сигнальной пушки, и войска, с разных сторон обложившие Москву, двинулись в Москву... (Толстой 6). ...(The Emperor) gave a sign with his hand. A single report of a signalling-gun followed, and the troops, who were already spread out on different sides of Moscow, moved into the city... (6b).
Пугачев задремал, сидя на своем месте товарищи его встали и дали мне знак оставить его (Пушкин 2). Pugachev went to sleep, sitting in his place, his comrades stood up and gave me the sign to leave him (2b). Pugachev fell asleep in his chair
his comrades rose and signaled to me to leave him (2a).

Большой русско-английский фразеологический словарь. — М.: ACT-ПРЕСС КНИГА. . 2004.