dont hesitate to ask any questions despite the fact that you dont have a Bonne. Great group of people there.
I think it would be the pump if it cant handle a load. 44 psi is good for the prime, but if it drops off, then the pump may be weak. Or you just may have a ground issue. The sending units and many cars use the tank as a ground. The lock rings, and anything under the car really, can become rusty. It has been in service for 20 years, so it just comes with the territory.