“The color palette used [for Phoenix’s ‘Joker’] certainly seems inspired by the makeup worn by John Wayne Gacy, a serial killer in the ‘70s who worked as a clown at parties and events. Gacy’s clown makeup also incorporated the wide red mouth and high blue eye paint that appears on Phoenix. The bright blue makeup around the eyes also seems to be a nod to the look that the Joker had in some of the older Batman comics, such as ‘The Laughing Fish’ and ‘Sign of the Joker.’” — Looper
“There are several different types of clown performance. Although, somewhat characteristically, The Joker doesn’t fit neatly into any of them, the villain does share much in common with the Tramp and Hobo types. A Tramp clown is recognized by his shaggy, unkempt appearance with red around the mouth to give an unshaven and burnt impression. Often seen with painted-on tears, Tramp clowns tend to wear ragged three-piece suits and the performer would usually use their own hair, ruffled up, instead of a wig. Tramp clowns have a sorrowful attitude and a resentment towards the world, while their Hobo counterparts look distinctly cheerier, characterized by a painted smile and more open eye shapes.
Generally speaking, the character of The Joker throughout his history has incorporated elements of both the Tramp and Hobo clowns, and Joaquin Phoenix’s makeup also shares several consistencies with the descriptions provided. The blue teardrop and wide, red smile mix together elements of the Tramp and Hobo types of clown, while his suit and messy hair embolden the image of someone down on their luck and angry at the world around them.” — ScreenRant
— Theories about the inspirations for Joker’s make-up in Joker (2019)