Mules take a bit more intuition & kindness to train. I worked with driving mules for a summer. They were not worked with all winter & wild in the beginning of the summer. They got better as the summer wore on & one young one ( most of them were 20+, he was about 10) that got injured got a lot more friendly during the time we kept him in a small paddock so we could catch him easily & work with him (well, me - the lady that managed the place was VERY lazy & did not do much).
Of course when he was turned back out in the some 20+ acre pasture with the 10 or so other mules & two big horses, he went back to his old ways.
Overall, I think proper ground work & training when a mule is young is so much more important than in horses. Mules seem to remember more & r much more likely to hold grudges, so to speak.
Like other posters said, a gaited mule is only half gaited - so he may not have inherited the gaits of the breed. Look for an older mule (7 years +). Make sure he is easy to work with & shows the gaits. Do NOT get a mule that needs a bit of 'reschooling, attitude adjustment'. Bad behavior is so much harder to correct in mules.
Getting a younger mule may be tempting so that u can train it yourself & not worry about correcting bad behaviors, but mules take a slightly different mind set to train & a younger mule may be harder to judge if he really has the gaits u r looking for. If u have someone very mule knowledgeable to help u train & can see the gaits, then a younger mule may be a good option.