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...