Daisy is definitely a socialite, ESE or SEE. She's just playing around with Gatsby the whole time, what she's most serious about is maintaining her way of life. Even if she does love Gatsby she has no intention of leaving Tom and running away with him.

Poor Gatsby is definitely Fi-POLR for not being able to see the kind of relationship Daisy will give him. He's also not at all grounded in reality. ILE sounds right.

Nick Carraway is LII, imo because though IEI seems likely, he is the narrator and the writing does not sound like an IEI. He is more of an analytical observer. This is also why he gets along with his mirror Gatsby, when others misunderstand him, and also the initial attraction to Jordan Baker who is LSI.

Tom could really by any angry A type, LSE or even SLE.

Myrtle as SLE is actually a genius typing, I agree totally.