NYBMW23,
This is for 3-series 92 thru 98 Trans models might be slighty different for 99 models hope this helps.
If your transmission is manual check The Back-up light switch on the left hand side of your transmission casing. I belive the back-up-light is control by a plunger-type switch.
1. First ensure that the circuit fuse has not blown.
2. Test the switch, discounnect the wiring connector, use a multimeter set resistance function.
3. Test circuit to check that there is continuity between the switch terminals only when reverse gear is selected. If this is not the case, and no obvious breaks or damage to the wires, the switch is faulty, and must be replaced.
4. Disconnect the wiring connector,than unscrew the switch from the transmission casing.
Auto Transmission Check your inhibitor switch/ reversing light swtich