OH!!! If vehicle is as shown in the Diagram above, you will NOT hear the fuel pump when you simply turn the Key to Run. Look below the words "7.5L Fuel Tank Selector" and you'll see "Hot in Start or Run" BUT the power has to run through the Oil Pressure Switch. Not started yet, no Oil Pressure, no Power to Pump. Through THAT path, that is. Now look to the right of "Selector" and you'll STARTER RELAY. That's the solenoid inside the fender well. On ours, it was on the passenger side right by the battery. Should be a Light Blue Wire on that Relay. That wire should show 12VDC when the Starter is engaged. Its job is to fill the Carburetor while the engine is cranking so there's gas there to start on. Once running, you release the Key to the Run position. The Starter Relay drops Open but the Oil Pressure Switch Closes, and power to the pump is restored, but through the Resistor. Many of us have run a pushbutton to the Blue wire so we could fill the carburetor before cranking. Much better starting that way.
But First!!! We need to confirm that your E350 is set up as shown in the Diagram.
