I personally bias toward PMs (or aspiring PMs) with a creative mind, whether that's shown through actual background experience in a creative field, or a highly creative or unconventional response to a question asked in the interview process. I find creative types (often with liberal arts degrees) to be highly effective PMs and leaders due to a common ability to connect dots and find problems and solutions others may not see or understand.
This is not a requirement for a product role, but I do think it's somewhat unique compared to what typical PM hiring managers screen for.