Green’s Dictionary of Slang

(US) drunk; thus phr. have a shine on.

1900		Sun (NY) 21 May 6/4: One might say, for instance, he is ossified [...] has a shine on, has a skinful.
1906		Salt Lake City (UT) 30 Mar. 4/5: He has [...] a shine on [...] an edge on.
1922		Appleton Post-Crescent (WI) 6 May 11/1: Flapper Dictionary JAMMED – Intoxicated, pickled, shellacked, canned, out like a light, potted, shined, drunk.