Q.My Burros Tail Beads On The Top Of The Pot Are All Splitting Lengthwise Then Shrivelling And Falling Off.
The burros tail is mostly very healthy and hanging outside with a bit of shelter from the sunlight. The top right side is suddenly shrivelling up and drying out. The rest of the plant seems healthy.

Certified GKH Gardening Expert
This specimen will appreciate being exposed, more and more, to full sun until it is in full sun all of the time! It will appreciate a slight dry out, but nothing like a true cactus would require. In fact, they will prefer to be on the moist side.
I would treat with a fungicide and start acclimating it to full sun. Here are some articles that will help:
https://www.gardeningknowhow.com/ornamental/cacti-succulents/burros-tail/burros-tail-care.htm
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm