Rear differential clunk when accelerating from a stop?

No problem, the first thing I would do is check the U bolts that hold the differential to the leaf springs. If you have coil springs, check the bushings in the trailing arms. Here are the exploded views of the differential and both suspension types so you can see what I am talking about. Check out the images (below). Let us know what happens and please upload pictures or videos of the problem so we can see what's going on.

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

You are welcome. Let us know what happens and please upload pictures or videos of the problem so we can see what's going on.

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.

Thanks for the images and video. Yep, those bushing look okay. I had a thought; the noise could be a dry driveshaft slip yoke. Please check out this video to see what I am talking about:

https://youtu.be/p2snOCyqVMY?si=PihVpHkbubI0mJhV

Can you please shoot a quick video with your phone so I can hear the noise? That way I can tell for sure what's going on. You can upload it here with your response.

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.

Oh man, that is wild. It sounds like you have a ring or pinion gear that is no good. I would remove the rear differential pumpkin-third member for inspection. Thanks for the video. a noise description would have been tough for this problem. Here is how to remove the unit which means the drive axles need to be removed as well. Check out the images (below). Let us know what happens and please upload pictures or videos of the problem so we can see what's going on.

PS. Can I ask which phone you have that you got the video upload warning? I can tell out dev team so they can fix it.

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?

You should be okay when logged in, thanks for letting me know. Can you run a test and upload the videos with your response please?

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

I would try ebay. Here is on for $427.00:

https://www.ebay.com/itm/134719888364?chn=ps&_trkparms=ispr%3D1&amdata=enc%3A1HoEsWXn6RVSiw0SqBm9tIw10&norover=1&mkevt=1&mkrid=711-117182-37290-0&mkcid=2&mkscid=101&itemid=134719888364&targetid=1644837435083&device=c&mktype=pla&googleloc=9031538&poi=&campaignid=20125739985&mkgroupid=149128855676&rlsatarget=pla-1644837435083&abcId=9312975&merchantid=419692524&gclid=CjwKCAjw69moBhBgEiwAUFCx2FWMcXw0SsOvbUUPSSxgpWQ8flXYNYNXp_CArFLxsT-G33hkFXg0nhoCHpUQAvD_BwE

Please let us know what happens.

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.

The disc or drum brake should not matter as long as the gear ratio and size are the same, did you get the old 3rd member out and is it damaged?

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.

I expected to see damage on one of the main gears? Was the vehicle in 4wd at the time and did you hear the noise coming from the rear of the vehicle?

It was not in 4WD. I have not tried to duplicate the sound while in 4WD.

That's a good sign, did you have any metal inside the differential after you took the third member out?

I do not know what you mean by "third member"?

There were no signs of damage and no metal shavings or pieces when I pulled the differential. There were no metal shavings on the magnet in the housing of any note and no fines in the bottom of the housing either.

I replaced the junk yard differential into my vehicle and had no change in the sound/vibration. I am now thinking it must be the transmission. I do not believe it would be the front differential as it is only engaged during 4WD isn't it?

Yep, I don't think it is the front differential either. It must be the transmission. I would try to service it first to see if you have any metal inside.

https://www.2carpros.com/articles/how-to-service-an-automatic-transmission

Please go over this guide and get back to us.