My wife and I passed by a winery with a pink elephant statue, and I cracked a joke about how this time, you knew you were drunk when you stopped seeing pink elephants, whereupon, I learned she'd never heard of that trope (and yes, that's a TV Tropes link). Explaining it to her reminded me of a short story I read when I was in elementary school (probably around the early 90s) involving an alcoholic who complained about seeing imaginary animals when he drank... but the problem was that other people were seeing them too! I don't remember how it ended, whether he got rid of the animals, but I have this memory of a line drawing showing him walking down the street with a parade of colorful animals walking behind him, rendered only as lines such that you could see the background through them. As I recall it was a pretty short story, probably less than a dozen pages. I read a lot of older sci-fi (the books from my parents' youth, on the shelves of the house), so there's a good chance that this, too, was older work.
Based on Organic Marble's suggestion, I checked out Tales from Gavagan's Bar, a collection of stories by L. Sprague de Camp and Fletcher Pratt. This review described "Beasts of Bourbon" (the name sounded very familiar) as follows:
"Beasts of Bourbon" - Asian metaphysics, despondency and bender don't mix, as a man finds his DT figments manifesting in the real world (most witty title of any here!) - Yellow Rattler cocktail, Daiquiri, rye & soda.
That led me to look for a more comprehensive review, which brought me to this LJ entry:
So, then. "Beasts of Bourbon" (from October 1951) is a barroom tall tale. We're loitering in Gavagan's Bar, presided over by old-school bartender Aloysius P.Cohan ("As long as a man can stand up and behave himself, he can have a drink at Gavagan's.") The conversation turns to d.t.s, the hallucinatory creatures serious drinkers are said to see. (Pink elephants are the famous variety.) Now, I did a good deal of bar-hopping and excessive behavior in my younger days but I can't recall ever knowing anyone who had actually had d.t.s or knew anyone who had. (folks who had transcendental acid trips in the 1970s, that's different.) Somehow, I don't think it would be an amusing experience but I'm not likely to find out...
Anyway, someone mentions a poor fellow named Campbell Van Nest who used to come into Gavagan's for a drink because his beasties wouldn't follow him in there. The strange thing was that he wasn't the only one who observed these bizarre critters. ("The animals out of his d.t.s,' said Willison. 'I saw them. So did you, didn't you, Mr Cohan?' ")
Sure enough, the next morning, a spectral tarsier is perched at the foot of his bed, peering at him with its huge saucer-like eyes. Van Nest is understandably dismayed, gets dressed and lurches out onto the street. Naturally, the d.t. primate follows him and, unnaturally enough, everyone else sees it as well ("Then he began to notice other people when he passed them, they'd do a double-take and give a grunt or a squeak or something.."). He is soon being followed by a curious crowd, his nerves break and he plunges into the sanctuary of Gavagan's. Here he finds the tarsier will not go, and it temporarily evaporates.
It's all downhill for Van Nest after that. More drunk than ever when he reels out of the bar, he plummets into bed and groggily awakens the next day to discover a second animal has joined the first, a maroon lizard with a frill around its neck. The more he drinks, the more beasties materialize and, frankly, they are getting less attractive each time....
I haven't found the illustration I remembered just yet, but everything else matches and reading the Archive.org copy of the October 1951 issue of Fantasy & Science Fiction clinches it.