I'd be wary of resisitance measurements when the DME is powered - I'd be inclined to measure the voltage between battery positive and pin 1 of the DME you should get 12 volts if the DME is switching.

A switch could be a short term measure but I would be concerned about the fuel pump running all the time, some DMEs switch off the fuel pump when the car is travelling down hill with the throttle closed and also after impact to stop the fuel pumping but not sure if the 5 series does this but I thought it did.