I'll try one more time to answer your questions. Some theory and facts: First you have already identified the problem. There is no fuel in the carb. The original carbs on this engine, either the Rochester 2 barrel or quadrajet would have a small fuel filter in the inlet of the carb. This filter would have a check valve, (for anti-siphon).
You also said the fuel pump is old. It also has a check valve. Modern gasoline is not friendly too the rubber parts in old fuel systems. The fuel pump must still work even if the check valve is leaking a little. But when you shut off the running engine and it sits a couple days the small leak in the check valve allows the fuel to siphon back to the tank.
Same problem with his Edelbrock. But replaced with a guadrajet fixed.....???
That Q-jet had a filter with a check valve.
I did not see a picture but I bet he has a newer fuel pump. More compatible with the crap fuel we have now.
I did not want to tell you to replace that old fuel pump because it still works. But with no second check valve and a most likely very tired check valve in the fuel pump, the fuel siphons down.
Summery: You identified the problem. You listed the possible cause, (fuel pump) and I just suggested an easy fix. Add the anti-siphon check valve.
@FireTruck1984 The exhaust manifold on the other side has no gremlins. One is not like the other.
@CoggedBelt75 I see a lot of things that could be dressed up a little. Driver's side, invisible front bolt on the intake manifold caught my eye.