Good news--splicing a T-tap ($3 from Autozone) and a 14AWG wire) around the broken pin into the module (soldered directly to the PCB) solved the problem.



The tailgate did not need any reset, although it did not work immediately.
I tried a couple of times and could hear faint clicks, then it started working properly.


It probably could benefit from a calibration, but then again, nothing should have wiped the memory from the factory calibration.