I work with former racehorses and transitioning them into 2nd careers, most TBs and STBs are not taught to stand still and moving off as soon as weight is felt either in the saddle or in the cart. Teaching them to stand is one of my first goals so I'll throw out what I do and see if that helps.
I teach the "STAND" command on the ground first. I hand walk, whoa them back (I do all voice commands as I do work with more STBs than TBs and driving is my passion) and say "stand" and ask them to stand for a few seconds, I praise and give the "walk on" command. I work for a few days on this until I can get them to stand quietly for at least 30 seconds.
Once I start mounted or driving work I have a 2nd person there to help. We start with them standing in front of the horse and I use a mounting block, and I sit down and I'm giving the "stand" command while my helper helps to reinforce that command. I literally sit, let them stand for at least 2 seconds, dismount and praise. I will do this for another 5 times or so trying to have a 5 second goal of standing before walking off. I do eventually wean them off of a helper but I would rather take my time and safely teach this important step.