For a long time people have placed enormous significance in the Blake poem The Tyger recited by Red John to Jane. We all (including myself) have looked for a million ways to connect the dots between William Blake and Red John and use this as some clue to his identity.
Perhaps it is not this at all. Perhaps when RJ recited the poem to Jane it was not to leave a calling card, but rather to give him a clue to the conspiracies going on within the law enforcement agencies. RJ may have nothing to do with this corruption, but he is aware of it and wants to alert Jane to this (cryptically, of course) as a warning to him to be careful who he trusts. RJ wants to keep Jane alive (obviously, saving his life here) and is absolutely in love with the game of cat and mouse. It is his raison d'etre for the last decade. So he must protect Jane so they can continue this brilliant mind battle. I don't even think RJ cares if Jane ultimately wins. I think he will take pride in being defeated, if he is. But he absolutely must continue this battle with Jane, and wants to preserve Jane's healthy existence.
So, perhaps the Tyger poem was a warning to Jane, and there is not in fact a relationship between the corruption and RJ. Why, for example, would they have a password which is from a Blake poem and is also something that RJ likes to recite? This just sounds odd. Foolish almost, like a bunch of kids in a treehouse thinking they are cool. It doesn't really fit the personality of RJ to my thinking.
So, I am starting to really think that RJ is outside this group, and his poem to Jane was a warning, not a ritual of his, or some game he was playing to see if Jane could figure out who he was.
So, who would this theory tend to support as being RJ? Somebody who could have knowledge of the corruption, but not be an insider to any great extent. That tells me Haffner or Stiles. Stiles seems to be the obvious choice for RJ if we never had the physical descriptions from Harker and Miller. But we must take this evidence into account, I suppose, and that leads to Haffner. The master surveillance man, with a wealthy business venture and enough ties to all the nefarious organizations to be able to have knowledge of this sort, and also be a manipulator of those within them.