This is the problem. Some power supplies gracefully lower voltage to limit current, but most don't. My suggestion is to use a DC to DC battery charger, and set it's maximum draw current. Something like the
Orion XS maybe can do it. It has a 17 VDC input maximum which I haven't confirmed is greater than what the Tesla's 16V battery system maxes out at.
One could hook into the cigarette lighter power circuit and limit to something under 12 Amps. Obviously one needs to share that 12 Amps with other loads. The power for charging would then be fed to the proper pin on the trailer connector, then the charger mounted on the trailer. Fuse everything. Shorts will happen.