It might be Patrick's father Alex.
He hasn't been on the screen that much, but he had some appearances.
Red John is good at manipulating people. Alex Jane used to be a psychic, together with Jane. And 'Tiger, tiger' might have been a poem he used to tell Patrick when he was young.
I can't think of a motive for being Red John, but he might have been angry with Patrick for something that has happened.
