1. In Season 2 finale when Jane meets Partridge, Partridge says "Hey, Jane. ****" It seems like the **** stands for "long time", but actually it is the same thing Red John says at the end of the episode when he saves Jane. 
2. Patridge and Red John voice resemblance.
3. Jane scares Partridge when he comes back to the room after he left it, Red John scares Jane when he appears at his left side after he seemingly left.
4. The Tyger, a poem by William Blake, the author of A brace of Partridge.
But still, the question would be what is Red John's/Partridge's (RJ) reason for not simply killing Jane? The answer is simple. RJ is a narcissist and a manipulator. Toying with Jane gives him a feeling of power which is multiplied by Jane's unsuccessful atempts to catch him. And what can get him more off than a fact, that the man who helps CBI to solve any case, and is getting pretty famous for that, is unable to catch him. RJ's precise methods (which Partridge as a CSI must possess) are winning against Jane's guesswork.