Take a little screw driver and turn the little screw below the head light knob to the right and disengage the daylight running lights. Then see if the problem is still present. My friend had the same problem on his 95 850 n/o, he always had the drl on, and when he turned of the drl his dash light problem ceased from being a cause of worry. Volvo's are very pleasent cars.

In my opinion, Volvo made 2 mistakes with the lights. The first, making the headlight/tail lights part of the DRLs. They should have been separate lights on the front of the car only.
The other was to allow the headlights to be automatically switched off with the ignition. It is not difficult to turn off the headlights when you turn the engine off.

I suppose you have a melted wire or fused contact inside the switch that keeps the instruments on all of the time.
I suggest that the next time you go to a salvage yard, pick up a "new" switch and a dimmer switch. It will be nice to have a spare.

Klaus
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Volvoless. Sold the R. There is now a void...