The only way to really test the valve is to take it out, reconnect it, put a plastic bag around it, and see if it sprays when you crank the starter.
It's possible that there is not enough voltage to open the valve. Suggest you test with a meter.
When attempting a re-start, there might or might not be current to the valve, depending on whether the the thermo time switch opened during the first starting try.
Cheers,
CT