The Oxford English Dictionary (OED) first defines the term as “ a tail like that of a cock’, or ‘a tail that cocks up’; the latter is the prevailing notion” and gives as its second as “A drink, consisting of spirit mixed with a small quantity of bitters, some sugar, etc. orig. U.S.” The first citations are all American with the oldest being one one from The Farmer’s Cabinet of April 28, 1803 “Drank a glass of cocktail—excellent for the head... Call'd at the Doct's...drank another glass of cocktail.” The second oldest reference from 1806 from the Hudson, New York Balance is even clearer. “Cock tail, then, is a stimulating liquor, composed of spirits of any kind, sugar, water, and bitters.
Also, according to the OED the Charles Dickens antedated the term in his 1843 novel Martin Chuzzlewit “He could..drink more rum-toddy, mint-julep, gin-sling, and cocktail, than any private gentleman of his acquaintance.”
Mark Twain described “ a cock-tail”: in a letter to his wife Olivia from London in January, 1874: ❡ “Livy my darling, I want you to be sure & remember to have, in the bathroom, when I arrive, a bottle of Scotch whisky, a lemon, some crushed sugar, & a bottle of Angostura bitters. Ever since I have been in London I have taken in a wine glass what is called a cock-tail (made with those ingredients) before breakfast, before dinner, & just before going to bed.” [i]
Shake all the ingredients with ice and strain into a chilled cocktail glass.
H.L. Mencken in his 1919 First Supplement to the English Language records many theories the origin of the word cocktail. He finally lists seven which he said had “some plausibility.” Mencken struggled with the elusive etymology for decades and wrote again about it in 1948 in the New Yorker magazine in an article entitled “The Vocabulary of the Drinking Chamber.”
Mencken reports that in the years since the Supplement “ … a great many amateurs have thrown themselves into the breach, and the result is a mass of surmise and speculation that gives the scientific student a lot of pain. I have in my archives perhaps forty or fifty such etymologies for cocktail , but can only report sadly that nearly all of them are no more than baloney.”[ii]
He then procedes to list as the “most plausible” The most plausible a theory launched by Stanley Clisby Arthur, author of “Famous New Orleans Drinks and How to Mix Them ,” a classical work. It is to the effect that the cocktail was invented, along about 1800, by Antoine Amédée Peychaud , a refugee from Santo Domingo who operated a New Orleans pharmacy in the Rue Royale.This Peychaud was a Freemason, and his bretheren in the craft took to dropping in at his drugstore after their lodge meetings. A hospitable fellow, he regaled them with a toddy made of French brandy, sugar, water, and a bitters of a secret formula, brought from Santo Domingo . Apparently running short of toddy glasses, he served this mixture in double-ended eggcups, called, in French, “ coquetiers .” The true pronunciation of the word was something on the order of “ ko - kayt - yay ,” but his American friends soon mangled it to “ cock - tay ” and then to “ cocktail .” The composition of the bitters he used remained secret, and they are known as Peychaud’s to this day. His brandy came from the Sazerac du Forge et Fils distillery at Limoges , and its name survives in the Sazerac cocktail, though this powerful drug is now usually made of rye whiskey, with the addition of Peychaud’s bitters, absinthe, lemon peel, and sugar.
As Bergan Evans, concluded in his quest to find the true source in his book Comfortable Words “One man’s guess, like one man’s cocktail, is just about as good or poor as another’s.”
[i] ❡(quote from “The Love Story of Mark Twain and the Woman Who Almost Tamed Him” by Resa Willis
[ii] H.L. Mencken, The Vocabulary of the Drinking Chamber by H. L. Mencken, New Yorker Magazine; Nov. 6, 1948)
 Bergan Evans, Comfortable Words. P. 93