What helped me the most was to remember that the pivot is a FOREWARD maneuver. I used to back my horse up to shift her weight, then pivot. My pivots improved 100% when I remember to pull her head slightly foreward and down to the right.
To start from scratch, I walk circles to the right, I want the horse to start getting used to stepping out of my space as I step towards them. I actually make the circle smaller and smaller, until I get one crossover, then I quickly jog foreward. Teaching them when they are moving seems a bit easier to me when they are first getting the hang of it.
Later, from a stop, I will step towards their poll, while holding the halter to keep them straight. You might need to push their shoulder over with your hand if they do not move over. Just try for a step or 2 at a time, and go from there. If they want to move that pivot foot trot foreward.
I’ve heard there is a showmanship video supposed to be coming out, I’m very eager to see it!