Back to the OP:
If you are referring to the red light in the dash that indicates the Parking Brake is on, then mine is doing something similar. I comes on when I make a hard left turn, particularly on cold mornings. The contact must be REALLY close and when centrifugal force pulls it slightly to the right, it closes the circuit. I've made sure the lever is all the way down, but it does it anyway. Nothing more than a slight annoyance right now, but if it gets to where it stays on more of the time, then I'll have to start hunting for it.
Hasn't always done it, just started this past Winter. . .