You can correct me if I'm wrong, because I'm not really sure, but aren't saddleseat horses gaited? Is your horse gaited? And if not, can you teach a non-gaited horse to gait?
You just said you wanted to teach him, so I'm kind of confused, lol.
Not necessarily gaited, but it depends on the division. 3 gaited div. is W/T/C. 5 Gaited adds to that the rack and slow gait. Pleasure divisions can ask for extensions, and Park horses usually have flashier action (even more so than most flashy saddle seat horses). I think that besides 5 gaited the only the Plantation Walker div. (TWH's only) shows gaits other than W/T/C or reasonable variations of it. Breed shows might change division titles. I've actually seen Friesian entries in saddle seat classes, really spectacular, and the division rules meant that they didn't have to rack or anything beyond normal (i.e. gorgeous) Friesian gaits.
A stubborn horse walks behind you, an impatient one in front of you, but a noble companion walks beside you ~ Unknown