Being sure the wire tested is correct is key. With the ground wire to the control side of the relay for instance, it will float voltage even though it is a ground wire.
If you do have 12 volts egressing the FP relay, and this happens each and every time you turn the key, put your meter across the electrical connector for the pump (it's on the front-top area of the tank). If you see the same results there, you should have adequate power to the pump so I'd replace the pump.
If the output wire to the pump was showing 1.2 volts, check the Common terminal for the relay. It should show 12 volts constantly. If it does while your output shows 1.2 volts, replace the relay or clean the relay terminals. If the load-side wire into the relay shows 1.2 volts, check the fusible link for the pump. It's just off the solenoid.
If you do have 12 volts egressing the FP relay, and this happens each and every time you turn the key, put your meter across the electrical connector for the pump (it's on the front-top area of the tank). If you see the same results there, you should have adequate power to the pump so I'd replace the pump.
If the output wire to the pump was showing 1.2 volts, check the Common terminal for the relay. It should show 12 volts constantly. If it does while your output shows 1.2 volts, replace the relay or clean the relay terminals. If the load-side wire into the relay shows 1.2 volts, check the fusible link for the pump. It's just off the solenoid.