In case someone finds this when doing something similar, here's an update on what happened after my last post. I celebrated prematurely. The lower voltage signal was not actually triggering the sub, at least not consistently.
Figuring that I did something wrong with the wiring inside of the amp, I ended up peeling open the wire between the stereo and the front door amp to splice into the 12V signal wire there. I used a needle tip on the multimeter to find the correct wire. It was the red one. I stripped some insulation, soldered on some nice silicone wire, and taped everything back together nicely. I did get 12V, until the wire was connected to the amp. Then I got the same reading as before, under 7V. I guess the trigger circuit has only enough current to trigger the front door amp, with major voltage drop.
I did have success using a cheap 12v relay wired to the Bazooka 12v power, which I believe is intended to trigger on 3.3 or 5v. That worked well, but the way it was wired, the relay was energized when the car was off, it drained the battery, and I ditched it.
I believe I could do the same thing with a transistor in place of the extra relay without hogging energy. I could probably open the amp again and grab power from the other side of the triggered relay, which can be heard clicking on with the stereo. I could also move the power for the sub to a circuit in the fuse panel which is off when the car is off.
I haven't tried these things yet because the sub hasn't been in the car. After adding the front door amp and speakers, nice new woofers, sound deadening and treatment inside the doors, there is enough bass for me. If I do wire it back up in a way that works I'll come back and update.
2001 9-3 base