This may be of no help but...
We have a NP-75D (diesel...and a noisy thing it is...
) Generac unit in our coach. When I start it, I have a pre-heat (glowplugs) function that also primes either the pump or the injectors or both(I can hear the solenoid engage and the fuel pump run). I have to press the pre-heat switch for about 20 seconds and then while keeping it pressed, press the start switch.
It always starts and then when either switch is released, it promptly dies. When I do this the second time, it stays running. This is the S.O.P. on our Generac unit. I do not know if it is supposed to work this way but that is how we use it. Perhaps we have a fuel prime issue. That is why I am thinking that on your gas coach, you would have a solenoid to run your Generac fuel pump and one to energize the solenoid for the starter.
Call the following number. They are an authorized Generac dealer/repair facility and the parts guy knows his stuff.
Schwalm & Associates