Occult investigator, mystery enthusiast, ghost hunter; these are all phrases that I am considering. But I was wondering if there was any ONE word that describes it perfectly.
You can generally add the suffix -phile to create a word meaning an enthusiast of something, so the word would be mysteryphile or mysteriophile.
However, this is not an established idiom -- they're not in any of the dictionaries I searched, and Google Ngrams doesn't have any occurrences. There are some people using them as handles on the Internet, though: there's a Mysteryphile Facebook page, and a Mysteriophile blog
But the word would be clearly understood, because the suffix has a well-known meaning.