This lady does a pretty nice job and description of what she's doing. https://www.youtube.com/watch?v=20x7glyFVBo
I think you have to use at least a one piece of yarn to hold the end of the braid. If the hairs are very short I've seen people make three braids at the top of the tail as though they are making mane braids with the yarn incorporated half way down each braid. Then Those braids are braided together as the start of the tail braid and they continue as you would normally. And others even use just two pieces and criss cross those all the way down the dock adding more hair each time as though they are french braiding with only two strands. Although that might only work for horses who have long hair at the base of their tails.
Heres a link to someone showing the braid with three individual braids to start. No description but you can see pretty well. https://www.youtube.com/watch?v=f1iUbV1zG5I