I don't see the year of your vehicle listed.....so I am going to just generalize a little here......
There is a recall for this part. Call your local dealer, give them your trucks VIN identification and let them check GM's records to see if the part has been replaced yet. It will be a free repair if it has not been replaced yet.
The fuel pump in newer model Chevy trucks have a variable rate of flow. The fuel pump control module regulates the amount of voltage sent to the fuel pump. Higher engine rpm's cause more voltage to be sent to the pump. Lower engine rpm's cause less voltage to be sent to the pump. Basically: Fuel flow is dependent on the amount of voltage the pump receives.........voltage is dependent upon engine rpm's.
Ok so, knowing this, the first logical thing to do is check the fuse associated with that fuel pump control module. Next, check the fuel pump voltage on the fuel pumps voltage input wire.
Orange/Black wire is the fuel level sensor reference wire
Purple wire is the fuel level sensor signal wire.
GREY IS THE FUEL PUMP POWER WIRE
Black is fuel pump ground
^^^^^ Those are the colors of the wires that operate the fuel pump module. The other wires not described monitor the FTP sensor.
Use a volt meter and see how many volts are on the grey wire at the end of the fuel pump wire harness. If you don't have power and the pump wont run, you probably have a bad control module. If you have no power but can "hotwire" the pump and the pump runs, you probably have a bad control module.