Green’s Dictionary of Slang

1. a jazz fan.

1938		P. Whiteman in Pittsburgh Courier (PA) 17 Sept. 11/1: Hold your hats, ’gators, here we come.
1941		‘Digg Mee’ ‘Observation Post’ in N.Y. Age 26 Apr. 9/7: Come on you ’cats’ and ‘gators’ too, follow me, till I get through.
1955		Roy Hall ‘Three Alley Cats’ 🎵 The old jukebox was blowin’ out the beat / The cats and the gators were shakin’ their feet.

2. any person considered to be in the swing of things; a good dancer.

1940		Pittsburgh Courier (PA) 10 Feb. 7/1: The male ’gators of Whyte’s Lindy Hoppers fell out of the flappers with the softs on their leads.
1944		C. Himes ‘Let Me at the Enemy’ in Coll. Stories (1990) 43: That boll was some ickeroo ’cause it was doin’ some steps I ain’t never seen an’ I’m a gator from way back.
1947		Baltimore Sun 22 June Magazine 6/4: Gator . . . a good dancer (or good guy).

3. a term of address used between two men.

1953

L. Durst Jives of Dr. Hepcat (1989) 1: Gator, take a knock down to those blow tops, who are upping some real crazy riffs and dropping them on a mellow kick and chappie the way they pull their lay hips our ship that they are from the land of razz ma tazz.