Both starter relay and neutral safety are possibilities,also dead spot in the starter.But if your not hearing a click from the starter I think it 's not there.
When the problem was occouring did you try shifting the trans to neutral?
B-in-Law sold his W/horse 8.1 so I don't have access to his coach or wiring diagrams. If memory serves me correctly and you have the Allison 5spd. trans. there were issues with water entering the connections at the side of the trans, and I can't remember if it caused , shifting or starting problems.
I'll make a few phone calls and get back to you.