We know that the origins of the cocktail, both the word and the thing itself, are topics for lively debate.
The first definition of the word in print seems to have been in The Balance and Columbian Repository on the 13th May 1806. Editor Harry Croswell described it as “a stimulating liquor, composed of spirits of any kind, sugar, water and bitters,” a definition that hasn’t quite stood the test of time.
In 1862 Jerry Thomas (that's him above) published a guide called How to Mix Drinks; A Bon Vivant's Companion. It contains 10 recipes for cocktails, as opposed to punches, cobblers and whatnot. Bitters seem to have been the defining element. I have a facsimile copy right here. It contains the Japan Cocktail – brandy, bitters, orgeat syrup and lemon peel. It’s hard to see what’s Japanese about that, but it was a different age.
However, I would suggest that one place you wouldn’t expect to find a ‘cocktail’ in any sense is in The City of Saints and Across the Rocky Mountains to California, a book by Sir Richard Francis Burton (above), published in 1860, i.e. two years pre Jerry Thomas. Burton was crossing what he called the American Sahara, and the book contains a footnote which manages to combine cocktail drinking with shrooming.
Very possibly you can’t see this very well, in which case let me transcribe: ‘There is another kind of cactus called by the whites “whisky-root,” and by the Indian “peioke," used like the intoxicating mushroom of Siberia. “It grows in Southern Texas, in the range of sand-hills bordering on the Rio Grande, and in gravelly, sandy soil. The Indians eat it for for its exhilarating effect on the system, producing precisely the same excitement as alcoholic drinks. It is sliced as you would a cucumber; the small piece is chewed and swallowed, and in about the same time as comfortably tight cocktails would ‘stir the divinity within’ you, this indicates itself; only its effects are what I might term a little k-a-v-o-r-t-i-n-g, giving rather wider scope to the imagination and actions.” – (A Correspondent of the New Orleans Picayune, quoted by Mr Bartlet.) Sir Richard Francis Burton; what a man!