Well........No
safe ones.....
This might not work on a Mustang due to its ground clearance. I have done it on a Jeep and a couple of trucks, but I was young and stupid.
If there is room, you can get under the vehicle while they push it. You need to be sure to put some kind of positive stops front and real so it it jumps out of gear it will hit something before it runs over you.
Best move would be to find an old style grease pit where you can stand under it while they push it.
Then you can put your hand on various non-moving parts and feel the noise, plus use your hearing to figure out what is making it.
The fact that you can recreate the noise without the engine running is a big help. Eliminates several things, and removes the noise masking it.
Failing all those ideas, the next best thing is to jack up the entire rear end and try twisting the back wheels back and forth hard while its in gear.
If its in the drivetrain, then you may be able to make the noise. If its in the suspension, then you will probably not hear it.
Just don't do like I did and tie yourself up under a vehicle and let someone drive you around the parking lot to locate the noise........
Years after I did that, I read where a guy tied himself under a big dump truck and let someone drive him around the parking lot to locate the noise.
After a few minutes the driver turned off the truck and asked if he wanted him to stop.
No answer.
Guy got out, found his boss wound very tightly around the drive shaft...........