Far as I know the parking brake is the auto park, this I believe is a separate system from your service brakes. I think the service center is blowing smoke.
HOWEVER, that said. I do not know the P-series brakes that well.
Question: other than the parking brake, which is usually A drum on the tail of the trnasmission... Are the service brakes DRUM or DISC.. on a vehicle of that vintage I"m not sure what is used.
I once had a 1992 Chevy Lumina APV. it had front DISC but rear drum. I had excessive brake pedal travel but NO leaks,, Factory Trained technican at the dealer went over it 3 times and never found the problem
Drums worn beyond spec. way beyond spec. I finally figured it out myself.