I know the 92-99s have a problem with those same displays. I'm not sure where the circuitry is for the VF displays in the 90. You need the wiring diagram from the factory service manual. On my car it is inside the instrument panel, which means the whole panel would have to be replaced. The climate control VF dimmer is actually inside the radio on 92-93 models.
But, on yours, I'm not sure. Wherever it is it sounds like the wiring to or from it, or the circuitry is going bad. Your headlamp dimmer switch and its wiring seem to be fine.
1999 540iA Sport
Former 93 SSEi Owner
Former 89 SE Owner