I started from the tail up. The peyote will be used for flat parts.
Three beads in a circle make two first rows. The first row of one bead, the second of two and the third created so that I took one bead, tucked one of the second row, added one more, tucked the other from the second row and added one more.
The same for the other rows. This is after the fourth one. The last two rows allways look like one, don't let yourself puzzle, just tuck every odd bead and the pattern will appear.
If you want to, you can thread the whole line at once:)
This way you either increase or dicrease the row's length - you can add a bead at the end or go one bead back.
And this is a herringbone. It has an even structure, you can see pairs of beads when working.
The stitch itself's very comfortable. You thread two beads, then tuck the next bead in the base row downwards and the next one back upwards. The beads are so handy angled that you may do it in a single move.
When finishing the circle you repeat this but in the end you thread through two beads upwards insted of one. Then the same cycle again: add two beads, go one bead down and one bead up and iterate iterate iterate.
This should be just a model to see if it would work, the real one should be threaded with a thin wire.