I would jack up the car, set the parking brake to lock the rear, unbolt the drive shaft and drain the rear of oil. When it finally has stopped draining, put a 1 & 5/16s socket on the pinion nut and using a breaker bar crank it back & forth while observing the movement of the carrier. You should be able to see movement in backlash, bearings, spiders, etc. And the condition of the gear oil would be a good test too. Shiny, glittering gear oil is not a good thing, DAMHIK.