Ok I know nothign about minis, but getting a horse to "trot out" is a requirement at the vet checks of an endurance ride, if the horse doesnt effortlessly break in to a trot you can get pulled by the vet, sooo its kinda important, we are also doing this with very tired horses, so we practice alot.
Initial training is at a walk give an attention getting command, I use verbal , some trainers wiggle the lead line, then you lean forward to give a visual command and start jogging, as soon as the lead line gets tight have a helper smack him in the butt with a lunge whip. Usually only takes a couple times and they figure it out. 1, 2, 3,,,,, three levels of asking, like most things horse related, ask , ask harder, ask harder, Generally I use verbal, mild physical, strong physical. For most tasks, but if you look at most trainers they are using some kinda variation of 1,2,3.