Green’s Dictionary of Slang

1. a derog. name for a civilian, as named by a soldier [a civilian’s mohair-covered buttons; a soldier had the unadorned brass].

1785, 1788, 1796		Grose Classical Dict. of the Vulgar Tongue n.p.: Mohair, a man in the civil line, a townsman, or tradesman: a military term, from the mohair buttons worn by persons of those descriptions, or any others not in the army, the buttons of military men being always of metal: this is generally used as a term of contempt, meaning a bourgeois, tradesman, or mechanic.
1811		Lex. Balatronicum [as cit. 1785].

2. (US Und.) an upholsterer.

1859		Matsell Vocabulum.
1895		C. Crowe Aus. Sl. Dict. 49: Mohair, an upholsterer.