Help identifying differential 65 Barracuda V8

Well that’s a relief to hear… factory sloppiness haha maybe it’s a “dummy clunk” to help remind me to be gentle on the tall skinny peddle on the right haha… I’ll give it a healthy cleaning, some new lubricant (gear oil recommendations?) and put it back together and hope for the best. Anything else that you might recommend I address while in the diff neighborhood?
You might also inspect the universal joints for play and I would also inspect the motor mounts and transmission mount, as these are other "clunk" producers when they go bad.