Ok, short run down as the what the computer is actually telling you.

The ECM (main computer) in Ford vehicles sends out a 5 volt reference signal to all of the on-board sensors and such. What happens to that voltage once it hits the sensor and comes BACK to the ECM is what the computer is reading. The Code 31 is telling you that the voltage coming back from the EVP (Egr Valve Position) sensor is BELOW what the computer expects to be seeing from it. This could be caused by a couple of things. First, dirty or corroded connections where the sensor plugs into the wiring harness can cause excessive resistance causing the low voltage reading. The sensor itself could have failed or be filthy (which still amounts to replacement in most cases). The same can be said for the TPS (Throttle Position Sensor). With both of these sensors the lowest expected voltage is 0.24 volts for the EVP and 0.6 volts for the TPS. The computer is getting voltage LOWER than that from the circuits that handle those sensors. Frayed wires, corrosion, and bad sensors can all be the culprits here.

Worry about the EVP and the TPS first because with faults at each of these, the computer has no idea how much fuel to send to the engine so it won't properly control the fuel pump circuit either as a result of the other two issues. Its a fail-safe situation. If the computer can't tell how much fuel to send, it just won't send... better that than sending fuel into a potentially dangerous engine environment. Since the truck will run under the certain conditions, its unlikely that your fuel pump has failed anyway.

Notes:

EVP location - on top of the EGR valve. Mounted with three screws and connected with a short pigtail to the main engine bay wiring harness.
TPS location - bottom of the throttle body. Mounted with two screws and connected with a short pigtail to the main engine bay wiring harness.
(This one sometimes is easier to remove with the throttle body separated from the intake but as I recall is not a necessity with the right tools).