is a reference to gingering, a practice for perking up an old horse by means of a ginger suppository so that the animal would "cock its tail up and be frisky", hence by extension a stimulating drink, like pick-me-up. This agrees with usage in early citations (1798: "'cock-tail' (vulgarly called ginger)", 1803: drink at 11 a.m. to clear the head, 1806: "stimulating liquor"), and suggests that a cocktail was initially considered a medicinal drink, which accords with the use of bitters.

Etymologist Anatoly Liberman