I just had one more thing I wanted to add.
I mentioned that this method works well for forward horses and go-ey horses.
I think that this is because most of the time (not all the time!) forward horses have a good work ethic and they like to work and they like to please.
By doing the stop and back up method, you are not just stopping your horse, you are giving them a whole other skill that your horse must complete. Much like a rollback or a side pass, it's making it more fun for a horse that really tries to please.
This is just my thought on why it works for more forward horses!