Sometimes, those are separate circuits. One to prime sending power straight to the pump and then after that, through the relay and inline with a fuel safety switch.
When set to on, test the out at the relay if you can find it. If you aren't sure, you could always run a wire straight from power to the fuel pump wire temporarily to see if power is your issue before you waste a bunch of time on it. but if you hear it stop or not running when it's supposed to be, that is the problem.