Green’s Dictionary of Slang

orig. used for gin; a popular method of drinking tequila, in which one places a pinch of salt on the back of the hand, licks it off, drinks down a shot of tequila and immediately bites into a segment or a slice of lime.

1931		Chicago Trib. 16 Dec. 10/2: For the swiss Itch. ‘Fill small cocktail glasses with ice cold gin, take lemon juice [etc]].
1939		Dly Jrnl (Vineland, NJ) 22 May 1/1: ‘Gin is poured into a glass. A lemon is halved [...] a quarter tea-spoon of salt is shaken [...] Then, in rapid succession the salt is licked, the gin gulped, and the lemon sucked. That’s a Swiss Itch!
1945		Capital Times (Madison, WI) 21 Oct. 30/5: After an entire summer golfing [...] we recently discovered what was wrong with his golf was that he suffered from ‘Swiss Itch’. This is a drink, not a disease.
1959		(ref. to 1920s) Life 7 Dec. 51/1: The technique [...] was [...] old stuff to mature Americans who in Prohibition days had used it, complete with salt, as the safe way to take bathtub gin, then called ‘Swiss Itch’ .
1965		Boston Globe (MA) 3 Jan. 67/2: It was called a Swiss Itch and, sure enough, that’s the way you drink tequila in Mexico.
1977		Valley News (Van Nuys, CA) 24 Mar. 77/1: You say you don’t know about a Swiss Itch? [...] You grasp a shot glass filled with tequila, vodka or gin [etc].