Many interesting theory on several charachter.
I think that Partridge has a lot of chance to be Red John. His voice is RJ's voice and his cultural references are important (A Brace of Partridge by Blake). I've report the facts and some deductions. We know some characteristic of RJ. I think, instead, that Kirkland investigate on RJ's powerful friends in FBI, and relationship of RJ with politicians and other powerful people, that put in danger the security of the Nation of USA.
Well.
Profile of Brett Partridge as RJ:
1.white male
2.mid-30s in 2003-40s now
3.just under 6'00' tall
4.medium build
5.works for CBI
6.speaks a little Spanish (link: possible he knows Tijuana's street/ Partridge said: que pasa dude?)
7.arson expert (talking very well on pretended "spontaneous combustion"; remember Todd Johnson)
8.socially awkward, especially around "normal" (not psychopaths) women (nervous with Lisbon, in Pilot, he touch many times his necktie)
9.forensics boss
10."Totally macabre", he love horror and blood
11. "Handled RJ cases"
12. He dislike PJ
13. Theatrical "appearance" and behaviour (it's his normal behaviour, but maybe he accentuates it to look a little clever, like the killer guy in the 1x09.
14 A little speech impediment (some letters: s, c, etc.)
15 graduate (biology or criminology, or forensic anthropology) and cultured (known literature: Dickens, Melville's Moby Dick)
Possible (theory and hypothesis/deductions, not sure facts)
1. Problem with his mother
2. Possible former Visualize?
3. RJ seems causes "shivers" and unlike feeling to the Prestons (mother and daughter in Red Barn) and the priest, and the house of Vogelsong the same to Lisbon, and also Jane, that don't believe in superstition. It seems that his instinct has the sensation that RJ/Partridge is here, inside; a similar thing happens to Rosalind Harker at morgue when was Carter's body.