OK. I think we're getting somewhere

This would also apply to the ground. I know you said that you double checked all the wiring but with two different modules doing the same thing, it really points to it. Maybe relocate the ground to a different chassis point. Where did you get the main power from? Ignition switch harness or battery? Maybe try to duplicate the problem by manipulating the harness where it plugs into the module (faulty connection to module).

Going a bit deeper into the troubleshooting you could also measure voltage with a multimeter. Between the +12v and ground, right at the module, with the door opened and closed (door switch is in the latch. Just engage the latch with a screwdriver or something). Ensure that the voltage is the same as the reading at the battery.

I've seen units try to start themselves dipping to as little as 9-10v, and as you mentioned most of the time can be traced to a faulty ground or poor main battery. Another possibility is that the white/blue wire could be seeing ground somehow, which is a negatively triggered activation input. Make sure the wire is properly terminated. A suggestion, I try to never spend too much time trouble shooting any one problem like that before I completely gut the unit and reinstall it from scratch, it usually ends up saving me time in the end if multiple problems compounded the symptoms.