This is everyone Jane has shook hands with in season 1 which is the season Jane most likely shook hands with Red John.I have put the names of the people and then in brackets is the person who went to shake hands first because I thought there is more of a chance that Red John went to shake Jane's hand first.I put this under Bret Stiles because I think its him but he never shook Jane's hand so I have watched it over again.

-Van Pelt(Jane)                        1x01        
-Dr Wagner(Jane)                       1x01            JAIL
-Preciado(Jane)                        1x08      
-Ben Machado(Machado)                  1x09            JAIL
-Jared Renfrew(Jared)                  1x11            DEAD
-A.P Caid(Caid)                        1x13
-Heather(Jane)                         1x15            JAIL
-Victor Marquesa(Jane)                 1x15
-Dan Hollenbeck(Dan)                   1x16            DEAD
-Randall Faulk(Jane)                   1x17            JAIL
-Mitch Cavanaugh(Mitch)                1x19 
-Drake Plaskett(Drake)                 1x23

I don't know what you think but I don't think that any of them are Red John and Iam surprised that there isn't that many Jane has shook hands with that are not dead or in jail.