If the “factory trained professionals” could not repair the problem, perhaps there is no hope of it ever being fixed. The absolute best indication of where the problem lies is with the wires that had burned the insulation and wiring insulation. The problem is not likely where the wires got burned, but down stream from that. I would cut those wires, not losing their ends of course and see what lights no longer work after cutting the wires. Because the lights or their wiring that no longer work after being cut are the ones burning those wires as they are lights downstream of the burned wires. And likely cutting those wires that burned would never cause another problem, except for those problem lights and wiring that no longer worked due to being taken out of the circuit.
Here is the other thing, what protects the wiring from the tow vehicle to its seven-pin socket connector at the rear of the tow vehicle? You say no burned fuses. However, might the circuit be protected by an automatic reset circuit breaker? I am here to say, if there is a short bad enough to cause all the lights to go out, it is bad enough to blow a fuse in a heartbeat. And here is the other thing, even if there is a broken wire that is shorting out downstream of the burned wires, that broken wire is not going to cause all the lights to go out, unless it is dead short that will burn a fuse in a heartbeat or open an auto reset circuit breaker until it cools. If the circuit is protected by an automatic circuit breaker in the tow vehicle, that would explain the lights working intermittently and since circuit breakers work based on heat caused by electric current flow, warmer weather will open a circuit breaker sooner than cooler weather.
The burned wires that were found are a clear indication that a serious problem lies with the coach and not the tow vehicle. The only thing that burns wires is excessive current flow due to a short circuit. Locating that short circuit if “intermittent” is not going to be easy. I worked with an old mechanic in the days of the old-style round glass automotive fuses. When he had a short he couldn’t find, he replaced the fuse with copper tubing and let the wires burn. I am not suggesting that ever be done on your coach, just that intermittent problems can be very very time consuming to fix. My experience over the years is they are usually caused by careless construction of mobile vehicles and I have seen a lot of stuff no one could ever imagine being done. It is possible one of the lamp assemblies or a bulb its self is defective (short circuiting). If an LED lamp is shorting, the whole LED can be defective. Those lamps to investigate are the ones that do not work after cutting the wires that burned. This kind of repair is best made by an equipment mechanic who understands automotive lighting systems. Sometimes the factory trained professionals get lucky and fix the stuff they build the second or third time around.
Sometimes, there can be two intermittent problems occurring at the same time. If there was an intermittent connection causing an open circuit in the tow vehicle wiring, 7-pin connector, or umbilical cord, that could also cause all the lamps to go out. In fact, there can be a short in the coach light wiring and an intermittent open connection between the tow vehicle and the first light on the coach. It takes a really good mechanic to fix these kinds of intermittent problems permanently.