Dash warning lights coming on

I purchased this car used. I noticed that the interior lights did not work. I checked the fuses and they were okay. I began checking the bulbs and found that all had been removed. Including the map/reading lights. When I replaced them with the correct part numbers, my airbag, parking brake, and traction control lights come on when I start the vehicle and stay on.

Oddly; when I turn on the parking lights, or full headlights, the warning lights disappear. However; when I turn the headlights on, the odometer turns red and issues a warning to "check brake system" for several seconds prior to returning to the odometer. Then the warning lights go off.

The engine and transmission seem to perform very well, and there are no other apparent issues.