Green’s Dictionary of Slang

still n.²

(US) a (quiet) drunkard.

1879		Yorkville Enquirer (SC) 27 Nov. 1/1: ‘Yas, old “Still-tub” ’ [...] and ‘Still-tub’ went into the doggery.
1896		Ade Artie (1963) 45: I ought to be out at the Washin’tonian home with the rest o’ them stills and hypos.
1909		J. Ware Passing Eng. of the Victorian Era.
1920		Ade Hand-made Fables 13: The Chatterboxes were glum and the Stills suddenly had Views on all sorts of Topics.

In phrases

have a still on (v.)

(US) to be drunk.

1887		Abilene Reflector (KS) 19 May 7/3: Gentlemen never acknowledge to being drunk. It is a ‘still’ or a ‘jag’ they have on.
1919		Salt Lake Trib. (UT) 17 May 6/3: To say that anybody could get ‘a still on’ by toying [...] with royal egg punches would be ridiculous.