I can't say about everyone elses Walkers, but Caesar (our TWH) would move into his gait from a trot or walk. If I'd wanted to keep him trotting I'd have to force it. Trotting was not what he would normally elect to do. Granted he was never trained for anything except pleasure riding. Had hoped to have him help with moving the cattle, but he was never on par with my QH for that. Best used from the back just to keep the group moving.
Even so, he was a great pleasure ride. He would gait the close to 5 miles to the intersection if I kept him above a walk. About the only time he elected to trot on his own was when riding with my QH mare and she was at a trot. We would trot and canter them together. None of it every caused him to not gait when I took him out by himself. At it certainly wasn't me, because I wasn't into any show kind of horse riding. I rode for pleasure, for going distance (30+ miles/day) and the work the cattle. The horses gaiting was purely on his own. The only thing I did to get a gait was ask him to speed up from a walk or slow down from a canter. If I did that I had at least a 75% chance that he was going to gait (for which I would lavish praise on him :)) )....and I was going to have a smooth ride. Although, I was ok with posting on those rare times that he might trot instead, or if riding with the mare.