At least on a 78, the fuel pump shouldn't run constantly with the key on like that. It's trying to build enough pressure in the system. My 78 with a new OEM pump will run the pump to pressurize the lines if it's been sitting a while just before I turn the engine over. I have a leaky injector (or two) and it hums until the pressure builds up. Maybe there's a leak somewhere in the lines that keep it from reaching enough pressure?
I recommend a gauge after the fuel filter under the hood. It will help you solve fuel delivery issues. I can watch the pressure build on an inline gauge from inside the car with the hood up.