First of all, thanks Arrow for your explanations. I appreciated them!
My horse (registered as a Kentucky Mountain Horse, although he has a lot of Walker in him) also does a walk, a flat walk, a running walk, fox trot, pace, trot, and we are working on the canter! I, of course, prefer the "true gaits"; after all, I paid extra for them!!
The ONLY time I let him trot is when I am not
on him, and he is in the round pen, just getting his muscles going. When I am on him, I don't let him trot ever. The way I do this is to slow him down just a pinch, press in with my calves a bit, and "massage" the reins gently; left, right, left right, This gets him back in gait in a matter of steps.
I can tell when he is pacing; it is smooth, but is more of a left-right feeling in my seat. Although his pace is smooth, I know it is considered "wrong". But seeing how my horse is for trail only, I don't mind, as long as it is comfortable for him, and smooth for me.
Many gaited horses canter a bit differently than non-gaited horses. Some (like mine) of them add an extra step in the back; almost like a bit of a fox trot with the footfall. When I first rode my horse, he cantered beautifully, but on my local trails, I don't have much opportunity to use the canter, so he is out of practice. I have been working on his canter extensively for about 4 months now. When done correctly, it is like a rocking chair; smooth and wonderful. Some gaited horses do it easily; some don't.
I also know that MANY gaited horses cross-fire when cantering, or easily lead with the wrong foot in an arena. Again, it doesn't matter on the trail, but I do want my horse to be balanced, so I work on it in both directions.