Recently I read that Tim Burton and Monica Bellucci love Federico Fellini movies.
Burton said Beetlejuice’s origin story was like the prologue to a Fellini movie, so it had to be told in black and white and Italian with an overall visual style like those in Fellini's movies.
One of Fellini's most successful films, Toby Dammit (1968), looks like it could have possibly inspired the appearance of Betelgeuse? Just a little hunch I had, since it seems Lydia's design was inspired by the witch in Mario Bava's Black Sunday (1960), another giallo movie which Betelgeuse's backstory takes reference from :)
Toby Dammit is a film about a debauched actor who is tormented by the devil, based on a story by Edgar Allan Poe. It could be totally off, but watching this film, his unique look, the painted white face, bleached hair and purple-shadowed eyes kept reminding me of Betelgeuse's appearance, especially now that we have seen his backstory.
It's interesting to watch all of the films that inspired Tim and infer what elements each piece of cinema contributed to his unique style, from visual motifs to narrative themes and character design.