I am following with interest. My Cummins does not always fire the starter on first try. (Click... but no starter. 2nd or 3rd try the starter rolls.) Since the starter was replaced a few weeks ago, it points to the relay you mention. I had planned to change it, did not know where it was exactly. I will look to see what is connected.

Sounds like the Gillig is set up similar to my Spartan. I too have a constant duty relay to energize the "ignition" circuits. (Actually 2 relays, one on back panel one on the front panel.) Check all your connections on those big common copper busses, many of mine were loose/corroded. Makes for intermittent failures that are hard to chase.

When it comes to 20+ year old vehicle wiring, there are those you have worked on and those you will work on.

I am planning a thorough redo of my wiring panels, replace relays and circuit breakers very soon. Chased the cruise control problems, intermittent power supply and no ground connection were the main problems...

Good luck with the wily electrons! May the voltage be with you.