I don’t know specifically about the Traverse or GM products, but on my Ford Fiesta, I put a six pin socket on front of the car. From there, the tail, brake, and turn wiring is then tapped into the car’s wiring harness using diodes that are sold for this purpose. The diodes isolate the power from the motorhome from that of the towed car.
If there are plug and play options for your Traverse, I don’t know. If you go to etrailer.com, they often have videos (with written transcripts) on how to wire in the lights on a particular towed vehicle. They can, of course, also sell you the items needed to do so.
2020 Sunseeker 2440DS Ford, Trekker cap, Topaz paint