Green’s Dictionary of Slang

a fool, an eccentric, a dupe.

1895		S.F. Chron. 6 June 11/5: He [i.e. a con-man’s victim] beefs an’ de bull con tries make a stall. It didn’t go, so I ribbed de rummy up to blow.
1902		T.A. Dorgan in Zwilling TAD Lex. (1993) 71: (Some Noble Pests I Have Met) Also the old rummy who gets in front of a car and walks his horse. {Ed Clearly not a drunk from the drawing}.
1914		R. Lardner You Know Me Al (1984) 96: I guess all these lefthanders is alike though I thought this Allen had some sense. I thought he was different from the most and was not no rummy.
1917		R. Lardner ‘Three Without, Doubled’ in Gullible’s Travels 222: ‘Why, you rummy!’ she says. ‘We don’t have to tell ’em why we want to learn.’.
1930		G. Milburn ‘The Stew-Bum’ in Hobo’s Hornbook 138: She played me for a rummy – and me – of course I fell.
1938		J. Weidman I Can Get It For You Wholesale 2: I didn’t want to get him sore, but I had to let him know I wasn’t a rummy either.