Not worth me trying to watch your vid with this computer unfortunately, but is he the horse in your avatar? Gorgeous boy! When God created horses, she painted the good ones!
^^^ I do reinforce positive behavior, like giving him pats or letting him eat when I way so or letting him chill out after I mount and flex him. I also give him about ten minutes in the arena to himself.
I would personally be using more positive reinforcement(Good Stuff, rewards) along with the negative(removal of Bad Stuff, release of pressure). I don't consider pats to be +R generally, because most horses IME don't actually enjoy that.
Also don't forget that horses learn by *instant* association and can't link cause & effect if the 'effect' doesn't happen *at the time of* the behaviour you want to reinforce, or at worst, within a couple of seconds. So for eg. letting him chill as soon as you mount may be a good negative reinforcement for mounting(assuming he wants to chill, not go), allowing him to eat on the trail may be an effective positive reinforcement for whatever is happening at the time you allow it, but while I'm not knocking you for doing it at all, ten seconds in the arena, let alone ten mins is too far removed to be reinforcing anything that happened earlier.