Are you writing that the right flasher isn't working on the tow vehicle? Or is everything working on the tow vehicle and the tight turn signal lights up but doesn't flash on just the trailer.
What was the issue with the back up lights coming on on the tow vehicle when it's not in reverse? Maybe that could happen if the 12 volt
power line from the trailer battery was wired to the back up light pin on the tow vehicle. That would mean your 12 volt
charging line isn't working on the connection and it would mean that the back up lights on the trailer never come on.
If your truck 7-way was factory wired, I bet it's wired correctly. An easy way to resolve it all is to buy a 7-way tester at the auto parts store and test the tow vehicle with that. Then, if your trailer 7-way plug is like mine I just loosened the plug and plugged it into the tester. With a 1 amp battery charger, I found all the correct trailer wires by testing them with the battery charger, and then I wired the trailer plug to comply with the tester.
Next I had a molded umbilical cord and I couldn't see the wires on the molded end plug. The colored wire chart was not useful to me in dealing with the cord and I had the privilege of reversing two wires on my plug after I noticed my trailer back up lights were on all the time, and my trailer 12 volt
line was only powered when I put the tow vehicle in reverse.
I had 4 elements to deal with. First, I had the tow vehicle 7-way plug, then the trailer 7-way, and then both ends of the umbilical cord. All 4 have to be right and all 4 use all 7 wires.
Just as a point of concern from experience, a previous owner of my trailer had disconnected the break away switch and stuffed the wires behind the panel. I believe my trailer had the original 1976 break away switch on it so I ordered a new one from Vintage Airstream parts company. The new switch looks like the OEM switch and fits on the OEM mount.
A good help to me in all my Airstream work has been the factory Service Manual I purchased from Airstream. I'd recommend anyone considering getting into self servicing and repairing Airstream trailers and vehicles to get one. The cost was $60 and it saved me from making mistakes that I'd have to re-do.
At first I thought everything's hard to get at on my trailer until I discovered that it's only hard to get at if I don't know where it's at . . . or how to get to it:-)