Ok, I got my hands back on the car today.

The 'bucket' was free of noticeable spills and debris, except for light dust and an old dime. No rust, slime, or goo.

I gently blew out the area with a compressor and captured as much as possible with a vacuum.

The park lock solenoid gets power and moves when the brake is depressed. It does not move far enough to disengage the lock function. We did this with the engine running so getting maximum voltage.

I used some silicon spray on the plunger, letting it soak for a bit and then depressing the brake multiple times to work it in. I also used a small probe to repeatedly push the plunger in as far as it could go into the solenoid body, hoping to push junk out the other side.

Now the solenoid fully unlocks about 1 out of 5 times. I'm not sure if that's any better than before, but it's not enough to be reliable.

We stopped there. It's not my car and I am not prepared to perform more complex surgery that could lead to unfortunate outcomes.

Now he has a very good idea of the issue and can explain it to his mechanic.

Thanks again for all the insights.