How good are you with a volt meter?
It would be good to be able to check the voltage path when it does not start.
The neutral switch can be jumped out, but to know, the car would have to be in the state of "NO START" in the first place.
There is going to be your real problem; getting to test everything when it is broken...not at the gas station, but in your garage. Because it doesn't happen all the time, you may end up chasing it for a while until you find it.
