an auxiliary electric fuel pump is a good idea on any carbureted vehicle, actually a very good idea. That said I'd try still want to find out what is the actual problem. Fuel should always present in the bowl of the carb. You should be able to disconnect the fuel line at the carb (say doing a old school fuel pressure test) and the car should start and run for a minute or two on the fuel in the carb. If it won't the next question would be why is the bowl empty.
Check, after 2 weeks of sitting, take off the air filter and work the throttle (WOT) several times. If you do not get a full squirt from the accelerator pump each time than the fuel bowl is almost empty. Some fuel may have evaporated from the summer heat, but most likely the rest dripped into the intake manifold. If it squirts good, note if the choke is fully closed at that point; it should be. If not just adjust it more "rich" and try to start it.
You mentioned having the carb rebuilt, Did it do that before the rebuild? It is very possible the carb may need looking into again if the bowl is going dry.
If you want to check the mechanical pump there are two tests, pressure on the outlet side and vacuum on the inlet side that need to be to spec. any old shop manual should have the procedure and some parameters to compare.
I hope this helps.
Jerry