Water Heater, Go out on me?

Agree with all! Remeber that the red light next to switch only comes on when the water heater doesnt lignt. If everything has been working then the light should never come on. I am saying this to remind you not to throw parts at the problem until you confirm it. You said you jumpered around the switch and the wh control made a clicking. Am I correct that you dont get the clicking without the jumper?
I had some similar problems a few years ago and had to replace the gas valve at the heater. Turns out there two different sizes of input lines, and of course nobody had my size in stock.