"light, two-wheeled carriage, usually drawn by one horse" (1791), also "small boat," 1790, perhaps imitative of bouncing. There was a Middle English ghyg "spinning top" (in whyrlegyg, mid-15c.), also "giddy girl" (early 13c., also giglet), from Old Norse geiga "turn sideways," or Danish gig "spinning top." Similar to words in continental Germanic for "fiddle" (such as German Geige); the connecting sense might be "rapid or whirling motion."
"job," originally in the argot of jazz musicians, attested from 1915 but said to have been in use c. 1905; of uncertain origin. As a verb, by 1939. Among the earlier meanings of gig was "combination of numbers in betting games" (1847). Gig-economy is attested from 2009. Related: Gigged; gigging.