I'm saying that the power for running the fuel pump should flow from the power source, which is the alternator.
The relay still needs switched power. The relay is an electrically powered switch. A small amount of current is used to turn on the switch. When the switch is on, it completes a high current circuit between the power source and the whatever you are powering.
Ideally the relay for a fuel pump would switch on with the key in start and run and have a roll-over switch which will open in a serious accident.
The power requirements to close the relay is small. Thats why I did not show the current flow in the second diagram.
Randomly an automotive relay off the internet,
this data sheet shows it will close when supplied more than 7 Volts. Thats why you can trigger it on either side of the ballast resistor.
It uses around 1.4 Watts. So will draw around 0.2 amps.
The fuel pump will draw what? 5 amps? 10 amps? 15 amps? depending on the pump.