Wiktionary
n. A mixed drink for which one does not specify the exact brand of liquor to be used.
Wikipedia
A well drink or rail drink is an alcoholic beverage served using the lower-cost liquors stored within easy reach of the bartender in the counter 'speed rail' or well. Rail drinks differ from "call" drinks in that the former are offered when a customer does not specify a particular brand of liquor when ordering a mixed drink. The terms "well drink" and "rail drink" come from the name for a bartender's workspace, known as either the well or the rail. In any given establishment, the rail/well liquors available may be known as the "house pours" or "house brands".
The actual liquors used by a drinking establishment will vary. A bartender's well may include at least one variety of gin, rum, whiskey, vodka, bourbon, tequila, triple sec, and vermouth.
Some establishments that cater to higher-end clientele or wish to project an aura of luxury choose premium brands to be their well liquors (thus offering a "premium well").
Usage examples of "well drink".
Carson knew that, if left to his own devices, the animal, might very well drink himself to death, or at the very least give himself founder.
So, although heaven knows when I'll get to see Ginny again, after this, and I'd rather be doing other things, I might as well drink.
We may as well drink as much as it will produce and save the other for the descent.