Green’s Dictionary of Slang

1. drunk.

1891		Brooklyn Eagle 11 Sept. 2/4: Rum-dumb, [...] stupid with continual drinking .
1922		S. Lewis Babbitt (1974) 83: Don’t faint with surprise if some of those rum-dumm liars get one good swift poke from Mike.
1923		N. Anderson Hobo 49: Often when they beg they are drunk or ‘rum-dum’. As soon as they are sober they quit.
1927		C. Samolar ‘Argot of the Vagabond’ in AS II:9 389: Rum-dumb is a condition of hopeless intoxication. A wino was a good-for-nothing vag who used to frequent the wineries and became rum-dumb on the wine he begged.
1930		‘Dean Stiff’ Milk and Honey Route 98: Any hobo may in the rumdum daze that sometimes follows a blowout lapse momentarily into the practice of mopery.
1962		Ragen & Finston World’s Toughest Prison 816: rum dum – Intoxicated to the point of foolishness.

2. stupid.

1907		Times Dispatch (Richmond, VA) 30 June 35/3: They called them Lobsters, Rum-dumb Bums, / And every mean old name.
1930		D.M. Garrison ‘Song of the Pipeline’ in Botkin Folk-Say 107: Where is that rum-dumb water-jack?
1939		J. Steinbeck Grapes of Wrath (1951) 144: Can’t get a word out of ’im. Jus’ rum-dumb.
1949		(con. 1943–5) A. Murphy To Hell and Back (1950) 197: After associating with you rumdum bastards, couldn’t make the grade in a two-bit whorehouse.
1967		M. Braly On the Yard (2002) 206: I was building a model of the state cap’tol. I figured when I got it done, I’d duke it on the gov’nor [...] then that unconscious rumdum bastard falls off his bunk right into the middle of it.
1975		L. Rosten Dear ‘Herm’ 152: She is not so rum-dum after all when smelling a rat in the haystack of gold.