I have a 2007 LT3 Tahoe and its having similar problem. I posted a thread on here to, so you can see the details on mine.
parking brake problems...
- My issue seems to be related to the parking brake release lever/handle thing. When I have the issue, usually if I pull/mess with the release handle a few times, it clears it out. Recently I had this happen and I couldn't get it to stop, so I placed a folded paper in the side of the release lever/handle to extend it a little and I haven't heard it complain since.
- I am planning on taking it in to the dealership to see what they can do about that. I will let you know the out come.