First, the pump motor is nothing but a long copper winding, it would be a problem if there were no continuity. The pump motor is likely working just fine.
My question is, do your brake lights work?
Unless the wiring diagram in the service manual is wrong (it very well could be).
When you depress the brake pedal, pins 1 and 2, and pins 5 and 6 should show continuity, pins 3 and 4 should show open. The reverse should be true when the brake pedal is released.
For testing purposes, when you are testing the switch out of its mount, when the switch plunger is pushed in, the brake pedal is released. When the plunger is let out, the brake pedal is depressed.
Pins 5 and 6 simply power the brake lights, there is no sensing going on for these two pins.
Pins 3 and 4 control the speed control circuit, if your cruise control works, these pins work properly.
Pins 1 and 2 are the brake switch sense, this input goes to the PCM.
If your brake and ABS light comes on only with the brake pedal being released, i'd really need to see the codes stored. Unfortunately, I think the ABS codes can only be read with an MDS or DRB scan tool.
I can take a guess and say that something is failing the power on self test.
In practice, when I turn on the car (by pressing the brake pedal) the ABS and parking brake light are off but when I release the brake pedal the lights come on.
I'm not following what you're saying. Are you holding the brake pedal when starting the vehicle? That isn't necessary in a vehicle as old as yours. If so, don't and see if the problem persists.