Engine compartment noise
The noise seems to be responding to loading from the engine rocking in the mounts however I had a similar noise in my 2005 that drove me nuts for about 20K miles. I was sure it was coming from the right rear but it turned out to be the front swaybar links.
They are plastic and they are crap! If you haven't replaced those disconnect one side and check for a loose ball end. As one of the other responders noted do not use a standard replacement. Mine are Moog, they have grease fittings and work fine. I am sure the ones the other person recommended are good also.