2000 Ford Expedition Parking Brake Panel Light

This year the brake warning light on my panel would come on and off as I was driving (with the parking brake off). It began in the winter when there was lots of snow (and seemed to ease off once the snow was gone and it began to get warmer). I first noticed it when I started the car in the winter mornings, but didn't worry since within 5 minutes it would switch off. I therefore presumed it was weather/temperature related especially sine it became much less frequent as it warmed up and the snow melted away. But in early Summer the light began switch on and off as I was driving, and the trigger often seemed to be my using the brake pedal to stop (at red lights, or an intersection etc.). Now, it is on all the time!

3 years ago I had the parking brake cable replaced and it still seems to work fine. Sine the problem started I have frequently checked/jiggled/repeatedly released the parking brake lever but it has never had any effect.

Any thoughts?

Thanks in advance.