Thanks for the suggestions.
The reverse light bulb & sockets look fine (no water or rust, filament intact), I’ll try pulling them both out, then replace one at a time to see if I can narrow it down.
Then, will try to trace the reverse signal wire from the trans back to the back-up light, looking for damage that could cause short.
I do not have a back up alarm. I think the only thing the reverse circuit does is activate the back up lights. Given I flat tow 90% of the time (and don’t use reverse), I can live without back up lights. I just need to fix the problem so my turn signals don’t go out.
Had to put RV away; will pull it out after holiday next week and investigate.
Cliff