The reason why the fuel pump stays on the entire time with the key on, is because you are using the acc signal from the fuse panel. That is why the fuel pump stays on, key on power all the time.
I would be worried if the car was in a wreck, then the fuel pump would stay on and catch the car on fire because your not using the correct signal wire.
In my previous post on this thread, i said for you to look behind the alternator, that grey wire with the black connector should be your signal wire for the fuel pump. IT will allow the pump to prime, then shut off, IF your stock relay on the pass side is working. The wire should be very short and will be sticking out of the drivers side valve cover wiring harness, the other short wire is the green connector wire, it is for the TACH signal wire.
Now, i assume that the gauge is still "working" goes up and down with more and less fuel correct? Even thou its pegged past full, will the fuel level come down after you have put 100 miles on it?
I think if the signal wire from the sender is pinched, the gauge will go to empty, if its unhooked, hmmm i forget.
Lets start there.
BW