The drink is severed in a large hurricane glass (which is required for the 4 shots of liquor in the drink and the juice). The glass is filled with ice and the ingredients are added. Sometimes some grenadine is added at the bottom of the glass and the ingredients are layered, other times, it is served stirred. Traditional garnishes are pineapple, and orchid, and a wooden back scratcher. I usually use a wooden spoon.
Harry Yee is attributed to be the original creator of this drink. The name of the drink apparently comes from the backscratcher that was originally placed as a garnish in the drink. I have found many variations of this recipe in various mixology books as well as various websites. Most of the versions I find nowadays seem to contain much less alcohol than the version that I originally found in a drink mixing book that a friend brought me from Hawaii in the 1980’s. I am almost certain that the modern versions have been watered down due to the excessive volume of alcohol found in the original. Through undergraduate and graduate school, I would make a Tropical Itch for my friends on their birthday. Usually this would place anyone well on the way to oblivion. A tropical itch followed by a Vulcan Mind Probe would usually make it an evening for anyone but the most serious of imbibers.
I found an interesting history of this drink by Rick Carroll: