Yes, it would read 12v on both relay power pins, but only with key ON.
The relay part is just 1 wire wound around a metal core, when it has power flowing thru that 1 wire it turns metal core into an electro-magnet, that will pull the contacts closed, the Load part of the relay.
All mechanical relays work this way, so do fuel injectors.
So if there is 12v on one end of the relay wire there would be 12v at the other end, but no power flowing, you need a ground at one end to get flow.
Check the EEC relay, that's what provides the 12v to the Fuel pump relay, with EEC(key) off there should be no power at the relay pins, so grounding relay wouldn't turn it on, it reads like it has 12v 24/7, which is not right.
Power would be on the Load pin 24/7, that's direct from the battery as it should be.
Pull out EEC relay, that should cut power to Fuel Pump relay, if it doesn't then some one has rewired it, wrong.
The 4 pins in Fuel Pump relay
Relay part
1. 12v from EEC relay to Fuel pump relay, only on when EEC relay is on, and EEC relay is only on when key is on
2. Ground from ECM, this pin would show 12v, if above has 12v and ECM is not grounding it at the time of the test.
Load part, clicks closed when relay part has power flowing thru it, so relay has 12v and a ground
3. 12v from fusible link to battery, 12v all the time, not on key switch
4. Power to inertia switch when contacts close