Good solution with the tint. We've been thinking about replacing the head units in both the 240D and my 242ti but new units are just so bright and multi-coloured they don't match our older cars. And we're picky. Might have to try your tint idea.

To answer your question above, I have a Sony that is about five years old now in my car, and it does dim the entire unit (display and control buttons) when the headlights are on. I think it also has three settings for the dimming, off, on, and auto.
But five years is a long time in the car audio business, new Sony's may or may not do this.

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1971 280 SEL
1981 Volvo 242Tic | 1980 Bertone Coupe