Does the body control module anything to do with fuel pump or would that be engine on a 2003 Saturn Vue.?

On a 2003 Saturn Vue, the Body Control Module (BCM) does not directly control the fuel pump. The fuel pump is typically controlled by the Powertrain Control Module (PCM), sometimes also called the Engine Control Module (ECM). The PCM monitors various engine sensors and conditions to determine when to activate the fuel pump.

While the BCM handles many electrical systems in the car (lights, locks, windows, etc.), fuel delivery is a core engine function managed by the PCM. There might be some indirect relationship (e.g., the BCM might need to know the ignition is on to allow the PCM to activate the fuel pump), but the BCM isn't the primary controller for the fuel pump itself.