What's up with my parking brake?

I have a 99 GS-R and every morning, when I leave, the parking brake light on the dash stays lit even though I disengaged the parking brake. About 10 minutes into the drive, the light will turn off. This problem will not reoccur until the next morning.

What the hell is going on? The only thing I can figure is, in the morning the brake is cold and/or wet from dew.

What do you guys think and how can I fix this?