You can remove the pick-up from the tank and examine it. If the pump hasn't been drawing gas, the fuel line will probably be dry. You'll have to visually inspect the line for bad spots, but at its age, you might want to replace all of the rubber sections of the line anyway.New idea about what to worry about is whether or not the intake at the tank is clogged. If I disconnect the fuel line where it comes into the pump, should I get any fuel drain there? And how can I poke at the inlet to determine if my problem is with a bad pump or clogged inlet/line? The tank used to have a leak on the bottom so it drained quite dry before I patched it, so who knows the condition of the inlet can be.
Do you know how long the leak was in the tank? It might have let moisture in, which could have developed rust. If that isn't checked, it will eventually damage a new fuel pump. You might inspect the tank's inlet tube for rust. Decades ago, I bought a '66 Fury for a driver. It had a rusty tank, so I installed another gas filter in the line just before gas entered the fuel pump. I had to replace the filter frequently, but the pump never went bad.