It is true that the first codes of a racehorse are established so that when the reins are shortened, it is synonymous with speed and progress.
There is not really a typical process except patience. The patience to introduce new codes.
After, when the racehorse is left alone in a career, with a saddle and a different rider position, it is still rare for the horse to look for the finish post although the contact with the mouth is more constant.
Apart from the patience, the reward and the strictness in the establishment of the codes, there is no magic formula ..
All The Best,