Rear differential clunk when accelerating from a stop?

Thanks! Will do as soon as I get home this afternoon.

I added some photos and video via my iPhone. Did they not load?

Apparently, they did not load from my iPhone yesterday. I have coil springs and have attached photos and video of the trailing arms on both sides. Although they are old and cracked a little bit, I don't think they would make the kind of sound/vibration/chatter I am talking about.

I attempted to get a video from the inside of the car hoping to reproduce the sound at least and could only get it to do it for a brief second. It was raining when I tried it, and the differential would "chatter" briefly and then the tires would spin on the slick surface due to the rain. I don't know what to think about that. I am stumped.

I accidentally loaded 2 videos of the same side. Here is the other side.

Yeah, I'll try to do that today.

These two have the sound/chatter I am experiencing. I sometimes get it worse. I don't know if the sound will be enough to tell.

OK, it's saying they are "Not a valid video file." now. Let's see if it works anyways.

I have an iPhone 11. I may not have been logged in when I tried to upload the videos and only thought I was. I haven't tried it again via my phone though. I email myself the videos and then upload them that way. They are still. Mov videos though so I don't think it should be a problem when uploading them if I'm logged in, but IDK?

Do you have a good place to get the proper ring and pinion for my vehicle? Seems hard to locate.

When removing the ring and pinion and housing will I also need to remove item 2 in the sketch provided? Also, my vehicle has disk brakes and the sketch appears to be drum brakes. Will that make a difference?

So, I went to a junk yard over the weekend and pulled a pinion and ring gear housing from a junked 1994 Trooper. I tried to pull one from a 2000 model Trooper and realized it was a little bigger than mine and the housing didn't look like it would fit. But I wanted to see if it was the same method to pull the housing as the 1994 model, so I kept at it to try to remove the housing.

1994 model removing item "2" from the exploded sketch you provided was only necessary on the passenger side.

2000 model removing item "2" was necessary on both sides of vehicle.

Another thing I noticed on the 2000 model and didn't notice on the 1994 model is that it had both drum and disk brakes on the same wheel. The disk brakes housed the drum brakes. That is the weirdest thing I've ever seen. Okay maybe not the weirdest thing I've ever seen.

I pulled the old differential out of a junked one and brought it home then pulled mine out. It seemed like the fluid was low but did not appear to be damaged.

I did not notice any metal of any type adhering to the differential housing magnet.

I will be putting the new differential from the junked trooper in this week, hopefully today. I plan on changing the fluids in both the front differential and the transmission as I don't believe they have ever been done.