I think that Patrick could be Red John. At least that's what writers want us to think.

I really have just one thing to add to all existing Patrick=Red theories.

As many have pointed out one possibility is that Jane suffers from dissociative identity disorder (DID). There are several dissociative disorders which are closely related to one another and if you have one there is great risk of having another. Patrick has already had an episode of dissociative amnesia/fugue in one episode so we know that he has a strong tendency to dissociate.