I recently installed the EcoHitch from Torklift on my 2020 M3. Install went smoothly (helps having a lift ;-) and the trailer lights even smoother. I used this adapter available from a private vendor on eBay:
Tesla Model 3 Trailer Digital Wiring Module (Trailer Hitch Lights Connector) | eBay
Very slick, plugs right into the Telsa factory plug noted above for OE trailer light harness. This module is as plug-and-play as it gets, requires no cutting/jumping/running wires and module is contained in a sealed housing. I tucked it behind the bumper crash bar and mounted it there with zip ties.