RE: BME 50
Floater-
Yes, it goes to ground. You could take it from the engine ground, twist it up with the rest of the wires and terminate it at the box itself, one of the screws will do (metal box-ground) or to the other end of the black ground wire. You'll have two black wires when done, both ground. I believe all it does is provide shielding to the main three wires coming off the hall sensor.