The voice of Brett Partridge and Red John is an exact match. Cue up Brett's scene in episode one of season one and then cue up the last episode of season two (where Brett also makes an appearance) and listen to Red John speak.
The voice is identical and is the same actor.
Brett is in the first episode of the series but does not shake Patrick Jane's hand in that episode. This doesn't mean he and Jane have not met previously and shaken hands then.
Brett is also in the final episode of season two where Red John saves Jane's life.
Though the voice print is a match and Brett Partridge is in two pivotal episodes of the series, the evidence is circumstantial at best to him being Red John as Brett Partridge has only appeared in two episodes with no more than five minutes screen time for both episodes. He's never shaken Jane's hand on camera and other than the voice match and some dislike for Jane there's nothing else tying him to Red John.
Evidence for:
1. The voice print is a definitive match for Brett Partridge and Red John.
2. Brett Partridge works at CBI and has access to their computer network and servers which Red John has compromised a number of times.
3. He's the same size as the description of Red John.