Bret Stiles is not Red John but he is Patricks real father.
Patricks happy memory was discovered by Red John , because either Red John was  ( 1.) actually there to witness  the memory or (2) Patrick was hypnotized to reveal information about himself.
Red John is Patricks brother/ or sister. ( the bad sibling, hence Tyger Tyger, and symmetry references)  I have not idea who that could be but I am sure this is about 'family'.
At a guess I would say his wicked, deranged little brother is  Brett Partridge ( son of Bret Stiles, same first name).