My new-to-me '94 GT wagon (manual trans) has a strange ABS issue, and despite searching through dozens and dozens of ABS-related threads, I can't find that anyone else has had this same problem...

When I start the car, with my foot on the brake pedal, the ABS pump will kick in a few times in short bursts in a somewhat random fashion, and then quit. After that, when driving the car, it will occasionally kick in again, but only when the car is stopped and with the brake pedal held down.
The ABS light on the dash is not on, and it does not come on when the system is acting up either, but it does light up with the ABS fuse pulled so I know that the light itself works. I tried to check for codes, but I couldn't find the controller? It's supposed to be under the front passenger seat, right?

For now, I have pulled the ABS fuse, and the car stops completely fine. But I would like to fix whatever is wrong.

The pedal moves down a bit when you first step on it, so I suspect the brakes might need a bleeding. Would air in the lines cause the ABS pump to cycle like this? Is the ABS activation triggered by how far down the pedal is?

Thanks