Back in the day when I was working as a mechanic. We had a LTD come in. The owner said that the local Ford dealership couldn't find the thumbing noise when he made a right turn. Took us 3 days to find it. One guy drove the car, and another sat in different places. What we found was a wrench hanging behind the rear seat, off to the left side. It was hung with mechanic's wire. With a note attached to it. The note said "I see you finally found your noise."
Or the guy who couldn't find where the smell was coming from.
Pulled up the carpet and found a half eaten lunch from the factory guy.
I would check the rear diff bushing. If you have done any hole shots. And banging the gears. That's where I would look first.