I have pulled the fuel pump from the gas tank, and have a new one. If I send 12 volts to either unit, they work. However if I plug either into the wiring connector at the gas tank, they do not run. The voltage at this connector is 8.2 volts. Is this the correct voltage at this location, or is it possible the relay is bad and I'm not getting the correct voltage?

The relay should feed 12/13volts to the pump.
With fuel pump hooked up in tank go back to the fuel pump relay and relay orange feed wire and check your voltage there.
Then check voltage out of relay on gray fuel pump feed wire.

You are losing about 4 volts someplace.
MT