An old trick we used to do and I still would if needed. . Get a couple of guys or perhaps even three or four pushing the rear end down. Working it really.

You might be able to hear the part during the rebound and identify it. It might even be a tired rear end isolation pad. Probably best tried both with the engine on and off but not certain. Your description to me sounds like a loose or worn mount for something. Hopefully your proximity to the noise being a lot closer might help identify it.