To OP: Did you figure this out yet?
Your fuel tank is vented through a charcoal canister. The tank should run at a fairly neutral pressure (ambient) and is vented for both vacuum and pressure through the charcoal canister and sometimes the fuel fill cap. If the vacuum vent(s) is/are plugged, the fuel tank will develop a partial vacuum as you burn off fuel. The fuel pump will cavitate and fail to pump if the pump inlet is under too much vacuum. (less than ambient atmospheric pressure) You mentioned in your OP that it runs fine after you vent the tank by removing the fuel cap. Try confirming that the fuel tank vents properly before throwing parts at it. It is an older vehicle, but, 62,000 miles isn't much for a fuel pump (with good maintenance) in that era.
Chum lee