I also have an RST and all I get on the trailer app is a light test. I decided to just try adding the module to see what would happen. I still just get the light test. To the OP, prior to adding the module did you only get a light test option or did it give you other options? I'm curious because I had trouble getting the plug into the module (thought it should have been easy) and I want to be sure I didn't mess up the harness in the process.
I had this happen to my 20 RST. I noticed there was a small leak and there was water coming off the track for the sliding window and running down the glass across the wires. The wires were really hot. I assumed it was the water sizzling on the wires because it only did it some of the time. Dealer took it in and replaced the window. Just got it back today so i'm hoping that solved it.
I've had a somewhat similar issue. If I'm listening to a Pandora station, it will sometimes play a second preset Pandora station at the same time. One of the stations will be louder than the other. If I then switch to XM when it is doing this it will play for at most a minute or so and then switch back to the double playing Pandora stations by itself. XM will be playing fine until it switches. If I go to FM it is fine. A tech heard and saw this when it did it after an oil change. He said to uninstall and reinstall Pandora. That didn't work. I took it back and they were going to a software update but they then said that GM says it is likely an issue with the USB cables that were plugged in and supposedly there is a bulletin on this. They say you have to use your phones factory cable. I don't see how this makes any sense but the cables have been plugged in the whole time. I got the truck back a couple hours ago. Going to see if it does it again without any cables plugged in.
Long post to say maybe try a different cable? I'll follow up if I figure anyting out.
Came to the forum today looking for someone with the same issue cause I don't really buy the answer....
Bob