The way my car's light-bulb warning light works is that, once triggered, it will stay on until the ignition is cycled through off. I had a bad brake light bulb, and the warning light would come on when I touched the brakes for the first time in the morning, and then stay on.
So, I recommend you check on two things:
1) Make sure the light-bulb warning indicator in the dash still comes on when the ignition key is turned to ON, but before starting the car.
2) Check all three of your brake lights.
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One scenario I'm thinking of is that your light-bulb warning indicator bulb has shot.
Ken300D