wag (n.1) Look up wag at Dictionary.com
"person fond of making jokes," 1550s, perhaps a shortening of waghalter "gallows bird," person destined to swing in a noose or halter, applied humorously to mischievous children, from wag (v.) + halter. Or possibly directly from wag (v.); compare wagger "one who stirs up or agitates" (late 14c.).
wag (n.2) Look up wag at Dictionary.com
"act of wagging," 1580s, from wag (v.).
wag (v.) Look up wag at Dictionary.com
early 13c. (intransitive), "waver, vacillate, lack steadfastness," probably from a Scandinavian source (compare Old Norse vagga "a cradle," Danish vugge "rock a cradle," Old Swedish wagga "fluctuate, rock" a cradle), and in part from Old English wagian "move backwards and forwards;" all from Proto-Germanic *wag- (source also of Old High German weggen, Gothic wagjan "to wag"), probably from PIE root *wegh- "to go, move, transport in a vehicle."

Transitive meaning "move (something) back and forth or up and down" is from c. 1300; of dogs and their tails from mid-15c.: "and whanne they [hounds] see the hure maystre they wol make him cheere and wagge hur tayles upon him." [Edward, Duke of York, "The Master of Game," 1456]. Related: Wagged; wagging. Wag-at-the-wall (1825) was an old name for a hanging clock with pendulum and weights exposed.