318 Fuel pump will not prime

I have a '69 Fury II, 318, all stock, 52K miles.
If the car sits for a day or so, it will not start due to lack of fuel. I know that the carb does leak off fuel.
The visible fuel filter above the pump shows that no fuel is being pumped while on the starter. I have checked the in tank sock, replaced all of the rubber lines, replaced the fuel pump,(twice) and checked for proper venting.
If I prime the carb (dump gas) it will start and the fuel pump will then keep it running. There is never a problem after it is running--no starvation on long hills, so I don't suspect the eccentric.
I realize that if the carb is dry, it will take some cranking to get the bowl full enough to start, but this thing never pumps a drop on the starter.
As a result, this car almost never gets driven, and it's a shame.
I have thought of putting an elecric pump on a switch between the tank and the mechanical pump to prime the mechanical pump just for startups. Would the mech pump pull through an electric pump when the electric pump is off?
Any help appreciated.
Greg

You have a leak on the suction side. Its very small and once the prime is lost the cranking speed is not fast enough for the pump to draw fuel.

I considered that a possibility, as well.
I have put the car on the lift and looked very closely for any wet spots that might indicate a leak, but couldn't find anything.
The steel line on the car is still the original, and therefore suspect, but I couldn't see any leakage.
Thanks

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I realize that if the carb is dry, Would the mech pump pull through an electric pump when the electric pump is off?

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b 4 you crank it if you take off the air cleaner will the AP squirt gas? Yes it'll pull fuel thru the elec pump