Brett Patridge was killed because Red John wanted to keep Jane busy by showing him a corrupt organization (Tyger Tyger) or maybe trying to imply RJ was member of that organization, that's why Red John let Teresa alive, he wanted her to "send a message" to Jane, the message was what Patridge said before he died(?) (Tyger Tyger), now with the detective death and the tattoo is the same thing: he is trying to confuse Patrick.