Where is the fuel pump module located?

That car with the 3.5 should only have a simple relay to control the pump and not a pump control module. The power comes in from fuse 30 and to the relay the relay is turned on by the smart junction box, Power then goes through the circuit and to the inertia switch and out to the pump. The common failures are in the connector at the pump that gets corroded and the grounds rusting.

Been there, Ford likes to play games on them sometimes. If you had the hybrid, you would have a module. The 3.5 stayed with the earlier system until the 2013s came out when everything got control modules.
What does it do when it refuses to start? Just crank over and nothing else. Do you have any type of scan tool? For the Ford family https://forscan.org/ is a great program. Get the recommended dongle and the standard version and you can do a lot with it. If you decided, you wanted to change things the extended version gives you more access than the factory Ford scan tool! With it you could plug it in and when it doesn't start you could see the live data showing things like fuel pump, crank signals and all the rest. Would also allow testing of things like the relay easily because you could turn it on and off while you were right next to it.