Green’s Dictionary of Slang

thirst; thus on the drinkitite, on a drunken spree.

1865		R.S. Surtees Facey Romford’s Hounds 117: [He] was more afraid of the lady’s appetite than of her drinkite.
1903		Sydney Sportsman (Surry Hills, NSW) 1/1: The promoters [...] reckon a bookmaker’s appetite and drinkitite to be twice as great as that of any other man.
1909		J. Ware Passing Eng. of the Victorian Era 118/1: Drinkitite (Peoples’: East London). Thirst. The struggling populace, who chiefly joke [...] over their struggles, having discovered ‘bite-etite’ as a jocose conversion of appetite — came naturally to give it a correlative in ‘drinkitite’. There is also grim satire in the application of the last syllable, which is the common word for ‘drunk’, hence ‘drinkitite’ as a pendent to ‘bite-etite’ is positively perfect.