There are 3 fuel pumps on your F150. You have a low pressure fuel pump in each fuel tank and the one on the frame is the high pressure pump. Take the line off the back side of the pump on the frame and see what the fuel pressure is coming into the high pressure pump and the frame. You may just have a bad high pressure fuel pump. When you turn the key on, the pumps will run for a couple of seconds and then turn off, that is normal. When the engine is running, they will run continuously. By taking the line off the back side of the high pressure pump, we can see if the in tank low pressure pumps are working. Let me know if you get fuel out of the line when turning the key from on to off a couple of times.
No, your problem is effecting both in tank pumps. One common problem is the fuel tank selector switch on the dash. Remove the switch and plug it back in to the harness. Turn the key on, you should have power on the RED wire when switched to the front tank and power on the BROWN/WHITE striped wire when switched to the rear tank. Remember you will only have power on these wires for a couple of seconds when turning the key on. Also check the connector to the switch, if it is melted or burnt, you will have to replace the switch and the connector and repair any burnt wires.
Below is the wiring diagram.