The brake light and the chip in the rotor are two different problems.
The chip in the rotor (without seeing the part) could be a casting bubble which cracked and fell off during all those heat cycles and surface pad pressures to the rotor? Something like this does not in any way make the brake light come on or stick on.
Go under the foot pedal cavity, and find a ratcheted looking brake switch that triggers the brake lights to come on when the brake pedal is depressed.
Have someone at the rear of the car tell you when the brake light goes on and off.
If the brake lights are on now, pull the pedal towards you and see if the brake lights go out? If they do, you will have to push the brake switch assembly towards the brake pedal again. This is a ratchet type design as I recall, and you will hear a few "clicks" which moved the switch back in position so the plunger is set deeper in the switch assembly to close contact with the brake light system.
I agree with Ken and Redman. Change identical parts as a pair. Changing just one rotor may cause a pull to one side when the brakes are applied.
