Multi-meter not making sense is putting it lightly (driver's side.) I'm doing same thing and had no problem with passenger side turn signal. The white plug for driver's/passenger's side lights has 4 wires, not the 5 listed above. Hope I can just ignore Backup/Green-White. If I get it working, I'll list the wire designation left to right with the connector clip up.
Regarding towing, Ford has to be confident of some size trailer (usually <1,000lbs) in all conditions in order to approve. The EV makes it a little weird so they don't. I'll pull light trailer in EV-Later mode.
Update: There are some strange voltage readings off the white tail light clip. I used a clamp on amp meter and pulled the light assembly apart as if I was changing the bulbs so I could follow the bulb circuitry. The ground/neg wire is the slightly larger black/white wire on the end. Next to that is the turn signal contact. The next contact is the brake light going to the bottom filament. The next/last contact is the tail light going to the top filament.
After all of that, my new Tekonsha (clamp on ferrite rings) doesn't work.