Hi, I have 3 good reasons as to why Brett Partridge isn't RJ.
1. Brett isn't smart enough to be RJ. RJ is just as smart if not smarter than PJ. Refer to season 5 episode 15 where patrick had to tell Brett that it was murder and not an accident. Even if you said RJ didn't want to possibly reveal himself to PJ it wouldn't make sense because that case was completely unrelated to a RJ case.
2. RJ has too much pride to let another person take credit for his work. Refer to season 1 episode 1 where Brett says, "classic Red John smiley." Now you might say he didn't want to give himself up or that he wasn't saying it was Red John just his smiley. which takes me to reason 3.
3.As established by Red John killing Patrick's wife and child he hates being insulted especially in public. So if Brett was RJ why would he let Patrick get away with insulting him in front of people multiple times? Even if you said he "likes" Patrick and doesn't want to kill him because he has fun with him would still not make sense because he could easily have killed Lisbon, Rigsby, Cho, Grace, or anyone he's close to to get back at him.
Thanks for reading my theory! Thoughts?