Clank....
Here's another possible cause. In the posi rear-end, the backlash between the side gears and the spider gears is set by the posi clutches. When the rear gets "worn" the clutches get thinner, and there is more backlash in the differential, not necessarily between ring and pinion. Here's how to check. Get both rear wheels up off the ground. Stick a screwdriver down through the vent on the rear, and it will "lock" the ring gear. Now try to turn the drive shaft. If there's slack, the slop is between the pinion and the ring gear, and you found the problem. If there's no slack try to turn one wheel. If the wheel will turn a little, that slack is due to excessive backlash between the side gears and spider gears. Replace clutches, much easier than replacing a ring/pinion, and it will make the posi work better. (I've only done this once, on another car with an 8-1/2" GM axle. The "preload" springs actually push th side gears away from the spider gears.) Clutch pack is relatively cheap, less than $100, I think. But it sure is a messy, smelly job!!