An info item: My 2006 GT had a rumble noise seemingly just ahead of rear wheels both sides, but more sensitive to light road bumps on the right. Dealership applied a rattle-finder device that has wired transducers that attach around over the car and read back on the source. It seemed to locate the source in the right front suspension. They replaced the strut and a rear shock. They had someone riding in the trunk trying to find it. No result. I asked what Ford tech at HQ had to say. "It is a known issue with this model."
About three months later dealership said bring it in. Ford had issued a service bulletin that replaces and interface part in the front struts. They fixed it and removed an item that was driving me up the wall. Took a while to find it but it worked. Bully for Ford Tech.
2006 Mustang Rear Rumble Noise 
