I re-watched episode 4x07, "Blinking Red Light", and I realized something amazing.

Jane cooperates with Red John in order to bring down a serial killer of teenage girls, because he had no clues connecting him with the murders.

Jane could make Panzer (the killer) a bait to Red John, and catch him in the act.
He didn't though.He preferred RJ to kill him just to get rid of him.

Here is my point: Jane knows McAllister isn't RJ, he cooperates with RJ in order to reveal the secret organization within Law Enforcement.(Blake Association)

-That's why RJ tells the poem "Tyger Tyger" to Jane at the season 2 finale.
-That's why RJ leads Jane to Kira Tinsley and the three-dot tattoo.
-That's why McAllister doesn't really know how RJ got the list and says "I'm psychic"

Red John was against this organization, probably because they copied his work,
or somehow irritated him.

No doubt there is a strong bond within RJ and Visualize.Maybe Stiles discovered the secret organization, and he tried to get advantage of it, by getting away with murders, no pay taxes and other criminal acts.It's not a coincidence that when Jane learned about the tattoo, the same time FBI started to chase Stiles, after all these years.They may suspected that Visualize is behind the reveal of the tattoo.(Kira Tinsley)

And maybe that's why Partridge died.(or faked his death, it doesn't matter).
He was either about to expose the bond between Visualize and the BA or he was just RJ that wanted to mislead Jane.

In conclusion, Patrick Jane and Red John are playing a game that both are forced to play.
-Jane wants revenge,
-Red John tries to avoid the identification.

So, in this game there are times where both of the players need to act together in order to continue the game.And that also explains why Red John wants to be friend with Patrick.