A6 Multitronic: Reverse Light Switch Replacement

Hi.
I currently own an A6 2.5L TDI with 120kW and a Multitronic transmission.
I have the following problem.

The reverse lights are not working. The fuse is okay, and the bulbs are fine.

MWB 5, reverse light relay disconnected.

The error is stored in the error memory.
17090 Step sensor (F125) - Unexplained signal.
P0706 - 35-10 Occasionally logged.

The reverse gear also didn't work; it only allowed shifting into it, but the car didn't move. The gear indicator was also flashing. However, the reverse lights are constantly not working.

Is there a separate switch for the taillights? Because the driver can live with the occasional occurrence of the shifting problem.
Or should I replace the control unit for the Multitronic system?
Best regards, Bolzer.