I have two Tennessee Walking horses who have been analyzed by Liz Graves for their biomechanics (conformation). They are totally different. (I highly recommend Liz for any gait issues. We had 12 horses who couldn't gait, and all 12 did by the end of the clinic).
One is long and lean and does a fantastic running walk and rocking horse canter. He carries his head very low. His neck is almost parallel with the ground, his face is on the vertical, and he has a head bob. He tucks his rear end under and has a big overstride. He has a good stride on the flat and the down hill. But he has a hard time adjusting his gait when he is with trotting horses, so he starts doing other uncomfortable gaits.
The other, a more stocky type ("Joe"), does a stepping pace. Very high head carriage with a big thick neck. His neck conformation makes it very hard for him to collect. I feel a definite side to side action with him, and if I don't, I know something is not right with his gait. His head actually bobs side to side also.
The most important thing is, do not let your horse do a gait you do not like. I find it very difficult to control this when moving out with other horses, especially trotting horses. The speed of the gaits is different. When I ride with gaited horses, they both do great, but with trotting horses, my stepping pace guy has a much easier time adjusting his stride to other horses. Occasionally we get all jumbled up and I am bouncing quite high out of the saddle, straight up and down, and I have to slow him immediately. Since I have learned it would not be natural for him to learn the running walk, we work on a nice stepping pace. You have to learn what it feels like, and stop him from doing other gaits. Sometimes I tell him to "Gait" and start calling out 1-2-3-4. I know it sounds funny, but it does seem to help.
The whole reason we own gaited horses is for the smoother ride, so why put up with a jumbled mess? When I bought them, I thought they just gaited naturally, but they don't, and you have to keep working with them on the gait you like, not what they can do. Just keep up the hard work, it will be worth it.