The solution to the show really is, how did Red John know the short list based on "shook hands" considering Red John would need to know every single person Patric Jane has every shook hands with.
We know Jane was mentored in the circus and taught his skills at a very young age, an important clue is that Jane was not the first or the last person mentored; he had a falling out over a scam. So Jane's predecessor in the circus was trained by the same man who trained Jane.
Red John is not doing a happy face, he's doing a clown face. Red John has an intimate knowledge of the Circus circuit and knows Jane's personal life far beyond the adult years (the death of a childhood friend and the Circus circuit suspecting they know who Red John is but not wanting to get involved in family matters).
So, we're looking for someone who is older than Jane. Now across to Gale Bertram, notice the name pattern: Patric Jane, Gale Bertram; Jane and Gale are unisex names, perhaps they were both named by the same person. The concept of a twin is pushed into people's minds by Red John, implying Red John has a twin, actual twin or mental twin? physically dead or just dead to him?
Red John has impossible access to the Police computers, uploading files in ways which defy standard capabilities. Red John has constant access to police headquarters and police resources. Police work for Red John so he must be capable of easily programing them. Police training has them obey orders from superior officers all the time, so it's easy to program a cop when they are predisposed to following your orders.
Gale was in the mall and sat with Patric, Patric was there to meet Red John face to face.
Basic process of elimination: we have already had an episode where Red John had to be 1 of a short selection based on clues, in that episode Gale was the final suspect. Assuming Patric Jane made no Mental mistakes (he's the mentalist) then we must accept Gale as Red John in that episode.
Now Patric has used his mental powers to once again generate a short list and again Gale is on that list.

The Red Team: The show is leading us to believe Red John is more than 1 man, he's a team of people. this is a false flag, Red John is mentoring these people and brainwashing them to believe they are Red John. This is his way of again trying to slip through Patric's mental trap. Red John has already convinced a person they are Red John, season finally had that man shot by Patric. He's a creature of habit and as he's done it once he'll try to do it multiple times.
Evidence of this is in the statement "have you met me before?" asked by Bob Kirkland who was clearly programed by Red John to the point of multiple personality disorder. Tiger Tiger. twins. only people with multiple personality disorder or a twin brother would ask if their face is familiar.

Back to Gale: I believe the original show's intent was not for Gale to be Red John, I think they altered the show when Virgil Minelli left. I believe Virgil Minelli was originally set up to be Red John but they needed to change that when Gregory Itzin
left the show. Hence Red John deciding to "retire". With a smooth transition they ultimately replaced him with Gale Bertram, who's appearance and character is very similar to fit the original goal of him being Red John. There are a few clunky aspects surrounding that transition which imply the character is essential to the writers original concept.

Kristina Frye: was not a mentalist, she was being fed information by Red John. By having us and Jane believe Kristina was a mentalist and then Red John "breaking" her, we are lead to believe Red John has mentalist powers far greater than Jane. Having successfully played that hand and "pulling the wool over Janes eyes" Red John has then found a loophole which allows him to appear Mentally superior to Jane. Knowing the short list of suspects is an example of this, Patric saying "it's a great trick" and Lisbon convinced he's a genuine psychic.

So we're back to the initial question, how did he know the short list? A fake list was set up by Patric on his wall, it was to catch an insider but Gale didn't fall for it because Gale being Red John knew the names didn't match the very broad criteria and could see the simple setup.
Only someone who has known Patric his whole life, but not been known by Patric, would be capable of knowing who Patric has shook hands with and only someone trained like Patric could perform the mental math to deduct an accurate short list.