What is the most important thing in connection with the training of the horse?
It is to teach the horse to work properly over its back. This means that the horse must learn to work with its back up/lifted.
The strange thing is if you search on the internet, there isn't really much to find on the subject. And often when you finally find a good text about it, the pictures do not fit. At least not in the way I would expect it should look like.