1884, American English, a commercial name, probably an alteration of earlier bazoo "trumpet" (1877), which probably is ultimately imitative (compare bazooka). In England, formerly called a Timmy Talker, in France, a mirliton.
Kazoos, the great musical wonder, ... anyone can play it; imitates fowls, animals, bagpipes, etc. [1895 Montgomery Ward catalogue, p.245]
Mostly "etc."