Just a fancy thought:

What if Red John uttered his grand words "the game is over and I won", and then shoots himself in the head?

I know it sounds absurd and serial killers usually do not commit suicide, but I wonder how Jane would have felt about it. No more personal revenge for him, ever. Would he bend over Red John and try to reanimate the man? Maybe he would, but it's too late, and then, while thinking about the final lovescene of Romeo & Juliet, he also kills himself.

Afterwards a dove and a pigeon slip by.