gad (v.)
"to rove about," mid-15c., perhaps a back-formation from Middle English gadeling (Old English gædeling) "kinsman, fellow, companion in arms," but which had a deteriorated sense of "rogue, vagabond" by c.1300 (it also had a meaning "wandering," but this is attested only from 16c.); or else it should be associated with gad (n.) "a goad for driving cattle." Related: Gadding.
gad (n.)
"goad, metal rod," early 13c., from Old Norse gaddr "spike, nail," from Proto-Germanic *gadaz "pointed stick" (see yard (n.2)).