The fact that the switch works, means you next need to look at the output from the switch to the relay, once the correct relay has been identified take out the relay and using a piece of wire plug across 30 and 87, this will power the screen direct with ignition on, with the engine running you will hear the engine note change as the alternator loads the engine.
A break in 1 wire will not stop the screen working all lines are fed from each side, so unless they are all broken they will work with power.
The relay could have "vorn heiz" written on it for front heat, or "vorn heiz fenster", front heated window, but looking on the legend on the inside of the fusebox lid will show you which one it is, the rear screen will be a squarer shape drawing and the front screen relay will be a shape like a wiper blade sweep area.
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