gadabout, noun -- apparently this word is from the verb "to gad" from middle English gadden: to be on the go without a specific aim or purpose. A gadabout is a person who flits about in social activity.
This may very well be distantly akin to gadfly -- any one of various species of flies that bite and annoy livestock (horseflies, etc.), or, alternately, a person who stimulates or annoys, especially by persistent criticism.
Perhaps that's too fanciful. In contrast, Merriam-Webster reports that gadfly is related to gad, the noun, Middle English for "spike," in turn from Old Norse, gaddr; related to Old English geard, rod.
Then there is gadwall, a kind of dabbling duck, and gadzooks, an archaic mild oath (perhaps derived from God's hooks -- the nails of the crucifixion). It seems these have nothing to do with gadabout.
Isn't the English language something?