Is it just me or does 35psi sound a little high? I'm around 28 with the same tire 35" KM2's

 

When you folded your stem over? Is your valve stem on the spare rubber? If your valve stem is rubber I believe that means you have no sensor on your spare. I believe a tire with a sensor in it has a metal stem.
There are people on here that have had there TPMS light come on when the spare was low. I don't have one on my JK but my wifes Liberty reads the spare, wouldn't they be the same system? I know my wifes reads it because the other day it came on and the only tire that was low was the spare. The light went off after I filled the spare up to 33PSI and started driving it to reset the TPMS.

 

Mine was on for about a 2 weeks even though all stock tires were at the correct pressure. Didnt seem like it turned off until I did some highway driving