wait (v.)
c.1200, "to watch with hostile intent, lie in wait for, plot against," from Anglo-French and Old North French waitier "to watch" (Old French gaitier "defend, watch out, be on one's guard; lie in wait for;" Modern French guetter), from Frankish *wahton or another Germanic source, from Proto-Germanic *waht- (cognates: Dutch wacht "a watching," Old High German wahten, German wachten "to watch, to guard;" Old High German wahhon "to watch, be awake," Old English wacian "to be awake;" see wake (v.)). General sense of "remain in some place" is from late 14c.; that of "to see to it that something occurs" is late 14c. Meaning "to stand by in attendance on" is late 14c.; specific sense of "serve as an attendant at a table" is from 1560s. Related: Waited; waiting.

To wait (something) out "endure a period of waiting" is recorded from 1849. Waiting room is attested from 1680s. Waiting list is recorded from 1841; the verb wait-list "to put (someone) on a waiting list" is recorded from 1960. Waiting game is recorded from 1835, originally in horse-racing.
When speed, not stoutness, is the best of a horse, quite a contrary system is practised. With such a horse, the jockey plays a waiting game; that is, he carefully nurses him through the race, so as not to distress him by overpacing him; as the finish approaches, he creeps up to his horses by degrees, but does not quit them to go in front till he sees that the pace has made them "safe," -- when he lets loose and wins. [James Christie Whyte, "History of the British Turf," London, 1840]
wait (n.)
early 13c., "a watcher, onlooker," from Old North French wait (Old French gait "look-out, watch, sentry"), from Old North French waitier (Old French gaitier; see wait (v.)). Compare Old High German wahta, German Wacht "a watchman." From late 14c. as "an ambush, a trap" (as in lie in wait). From 1855 as "time occupied in waiting;" 1873 as "an act of waiting." From the sense "civic employee responsible for signaling the hour or an alarm by sounding on a trumpet, etc." comes the old sense "town musicians" (mid-15c.).