Red John is a man and he is left handed I have checked with every male on the list could not find any male who was right handed but my theory of him being left handed is from a scene heres the screen cap

http://images1.wikia.nocookie.net/__cb20121001235855/thementalist/images/thumb/1/13/
Roy_Tagliaferro.jpg/1000px-Roy_Tagliaferro.jpg
 
Jane doesnt ever hold his tea with his left hand. Holdin tea with your left thats a typical sign of being left handed.

http://25.media.tumblr.com/tumblr_lfgbopMSWZ1qflbkno1_400.jpg