If that pump is what I think it is there are two or three failure modes
Pump consists of a diaphragm, spring and a pair of check valves (inlet and outlet) and an electro-magnet and a switch
When the diaphragm is depressed enough (By the spring) the switch closes, energizing the magnet, pulling up on the diaphragm and "Sucking" fuel from the tank via the inlet check valve,, When the diaphragm is fully retracted, the switch opens and the spring then pushes it into the carb via the outlet check valve
Possible issues in the pump itself include failed check valves (Rare) perforated diaphragm, (not as rare but still rare) open coil on the magnet (also rare) and dirty switch contacts (I suspect this is failure mode #1)
To fix dirty contacts... IF you can open the body of the pump, use a contact burnishing tool.
If you do not feel comfortable doing this.. Don't try it.
I used to have a car with an impossible to find fuel pump that.. Wore out.. I popped on an electric, exactly as described above.. Had to clean it a couple of times before that car hit the recyclers.
Really liked that electric pump.. I mean
Cam shaft pump.. Hit starter, Grind, Grind, Grind, Grind, Grind, Grind, Grind, Varoom
Electric pump. Turn key to on, pause, hit starter Grin-varoom