I second the need of a volt meter
one thing you can do that's a "Cheap test" is lock the fridge on gas and fire up the genny. if it now lights and holds good chance it's a voltage issue.
BUT
The spark gap should be set for about 1/4" as I recall (PLEASE DO NOT TAKE MY WORD FOR THAT) is about 800 volts AC if the chart I googled up is to be believed. now I'd want about 1,000 volts AC to insure a good spark. if the battery voltage is too low ***OR*** the gap is two wide.. not happening.
I've not seen that on RV Fridges or water heaters.
I have seen it on two furnaces. My RV and my parent's Oil fired house.
Out of 2 I've worked on.
