Try changing the rear dif
oil (with the proper straight weight) and adding friction modifier. This solved all my rear differntial noise. I suspect the problem, if it persists may be difficult to diagnose. Pushing in the clutch is the ultimate in deceleration, ie changes the load on all components aft of the clutch. As the trans is still spinning (it is hooked too rear wheels after all), the noise could be in either component. Assume you've done the obvious undercar checks for loose bolts and rubbing marks. The chart above is a good go/no go way to elininate some potentials though.