Mitchell,
You may have found a solution to your problem, but allow me to share what little I have learned: I have a 2019 Siverado LTZ. Like you, I had a trailer light problem. Actually, I have several problems. I have a utility trailer which has all LED lights. My truck tells me that it is disconnected, if it even is hooked up and the lights occasionally work (They all work when I'm pulling it with my wife's Ford Escape, ALL THE TIME). With my flatbed (with brakes), the truck says it is disconnected, but all lights work (incandescent). My boat trailer has many lights and the truck and lights work as they should. Haven't tried my car dolly, but assume it will not work because it has few lights and all are LED.
First, went to my dealer, telling them about my trailer and how the lights worked with my wife's car. They replaced the module, with the tech saying he hadn't had to replace one before, but lights on utility trailer were working. I pulled the trailer two hours from home and was miserable for the entire 4 hour round trip. I kept getting error messages on both my info screen and the console in front of me. Driving on the Interstate, it is a wonder that I wasn't killed while being distracted, trying to dismiss the messages.
I found a forum online and there seem to be several solutions, all which will cost ME money.
I went back to the dealer and the tech came out and explained the issue. According to him, the trailer must pull at least 55 milliamps before the module will acknowledge the presence of the trailer. My utility trailer, with all LED lights, only pulls 40 milliamps, hence my problem. He thinks that if I can add a resistor to my white ground wire, my problem will disappear.
I told him to PLEASE tell Chevrolet that it shouldn't be my problem, because it is their problem. Remember the old days when we hooked up our trailers and the lights actually worked?? If enough of us scream loud enough, maybe they will come up with a solution. It is their engineering which created this issue. THEY should fix it!
In the meantime, I think I will try adding incandescent bulbs to my utility trailer to up the draw. Of course, I will have to have my lights on, all the time, for this plan to work. We'll see.....