How can a switch that is in parallel with a lamp affect the lamp?
Don't have enough rep or I'd just comment, but when you get back and have a multimeter, I'd check and see if there is any connection between pin 5 on the controller and pin 2. It looks to me that the wire connecting the lamp to L1 or N may be damaged in some way and it is finding a path through the controller (intended or not).

Also, what kind of problems are you having with the kiln? Or is it just the lamp malfunctioning?