Vampire

I have an 86 coupe. It has recently developed a mechanical squeak (as opposed to a dashboard squeak) somewhere in the rear of the car. Sounds like a hamster cage with wheel that has not been oiled. I have a loud exhaust, so it has been hard to pin down. It happens when driving and is not related to motor speed. It is intermittent, but I hear it more at around 50-60 MPH. I have not heard it at idle. If I push in the clutch it does not change, as soon as I touch the brakes, it goes away, and stays away for a little while after releasing the brakes.

What is this?