Violet and black is the lead that provides the input to the gauge from the sender unit.
Red and yellow is the power supply to your lift pump.
I may have the wrong diagram here, but are you sure the other lead is brown only? Or is it black and brown?

If its black and brown then I'd have another look at the wiring diagrams as I don't think it'll be a straight earth........according to the above diagram, it goes to current track 124, not straight to earth.
Main fuel pump will hum all the time..........that's normal.