Green’s Dictionary of Slang

(US) of a shop, police post etc, run by one person.

1918		Dly Arkansas Gaz. (Little Rock, AR) 19 Apr. 16/3: A white-enameled, glistening, ‘one-armed’ restaurant catering to government clerks .
1927		‘J.M. Hall’ Anecdota Americana I 108: The waitress in a one-armed beanery determined to have some fun with a patron.
1952		L. Lariar Day I Died 85: A regular restaurant [...] not high class, but no one-arm dump.
1959		H. Ellison ‘May We Also Speak’ in Gentleman Junkie (1961) 27: Hank walked into the little one-arm grocery.
1968		in N.Y. Mag. 6 May 24: He’s sleeping in bed and I’m freezing my ass off on a one-arm post.
1974		G. Radano Stories Cops Only Tell Each Other 59: I was on a late tour, a one-arm post about a half a block long.
1995		G. Radano Pigtown 289: He sat on the bed, staring trancelike at his shield, remembering his first tour on the street: a one-arm post on Lexington Avenue.