Fiona Apple is EII - don't let the fact that both of them are singer-songwriters fool you
Anyway - I thought I might explain myself why I think she's not IEI. Purely coming from VI, she lacks that ethereal IEI look - to me, she looks much more like an ExE. What's more, she seems to be really working her way throughout her own experiences of pain, trauma, sadness and idleness. I find her much too 'scattered' to be that sweet INFp that everyone loves. If it helps - and I know some people don't like to type others through their work - her lyrics are mostly about personal experiences and stories, and a lot of the recurring themes revolve around personal transformation and catharsis. IEIs tend to write more about time itself, her focus is mainly on the tragedy of life. ExE from me.