I have one of these** (maybe) and in addition to being fair, clear, precise with the ride and the praise, there are is an exercise and also a way of looking at the mental training for this kind of horse that might help.
Sorry for the complexity of what follows. Take what you like and leave the rest.
** I have a sensitive, forward-thinking mare who (also loses her balance easily and thinks that running to catch up with that will help (not)), that taught me how to ride and teach this kind of horse. But she is quite alpha and has a great deal of ego-strength; she has almost always thought of herself as a grown-ass woman and quite in charge of her own self-preservation. So this horse is brave, with a caveat: If you don’t teach her how to confront what scares here with slow feet and active contemplation of the thing (whether a moving cow, a still alligator-shaped log, or walking in a good, engaged frame under saddle), she’ll choose her own way. If she can’t turn and leave, she’ll stay there, but stay tense.
Your gelding might be less alpha than this mare. But the point is the same: By the time they are in tension, they are showing up mentally as best they can, but the task being asked fo them (and something that’s slow or still is especially hard for the worried flight animal) is scary for them. They are demonstrating courage and a work ethic just by not exploding and mentally staying in connection with you, even if the tension feels like it’s in the way to you.
So to me, the problem is really to get them to accept the psychological discomfort of being a student. All horses have to learn how to accept training, along side the process of learning whatever particular things we are teaching them. The tense but obedient, smart, “trying” horse gives the rider an opportunity to think about the horse’s experience as a student.
With the tense horse, then, they have to learn how to wait for directions, rather than guess about what we want (usually with too much “running off” or forward-thinking), or remain obedient to our aids, but not peaceful in the moments between them. The relaxed horse has this “wait for directions” part of being ridden figured out. And they have to have faith that when directions are given and followed, they will be made more comfortable-- put into better balance (that’s priority one to a flight animal being ridden by someone whose center of gravity is even higher than his own) and put into a situation where he gets the right answer and earns praise.
So my tense, forward horse, for example, had to taught to walk at the speed and kind of contact I wanted. That was hard for her at first. What helped there was me counting out loud the 4-beat cadence of her walk. I didn’t do this for long stretches, but somehow counting out loud helped my body establish a rhythmic walk and her body followed suit. An NH-style cowboy taught me about counting the rhythm of the gait you want and it works really well. Your body conveys that rhythm faster and more smoothly than can your hand, leg and seat when you consciously try to correct the horse; you are always a foot-fall behind what is happening. The horse hears your voice and it’s rhythm that echos what they are feeling from your body, and, especially awesome with the tense horse, you will be able to create the rhythm without the rein aids that can make the horse feel claustrophobic in and thus more tense.
And you also have to teach them how to mentally “hang in there” at any speed. A couple of pros, a dressage BNT and a No Name Trainer with some good skill and horsemanship both had me work on the canter with my tense runaway mare in a particular way. We’d ride a pattern with transitions in it and she just damn well had to execute those transitions where they came up, whether they were good quality or not. We did not canter for long stretches, so she didn’t have a whole lot of time to both lose her balance and get her adrenaline jacked up by that. The patterns went on for, say, 5 circles or 4 rounds of a figure-8, with the transitions happening in the same places. So the smart horse started fixing her own balance in the places she knew a transition was coming. That meant that my ride could be softer and not so much of an “assault” on her balance. Not realizing what she had brought to the table by maintaining her own balance, her experience of this ride was that when she kept thinking and listening to me, the ride got softer.
But she also learned that the pattern-- where she’d find peace because it was repeated and therefore predictable to her–was going to continue, regardless of how she felt about that. That was good for me, too. Horses and people can’t be allowed to bail on their job just because it gives them momentary and fair or normal, short-lived anxiety. That’s because the nature of accepting instruction naturally entails the uncomfortable feeling of not knowing whether or not you will succeed. So we can try to give the horse a better and better ride, but they also have to learn how to look for that better ride even if it starts out rough and scary for them.
The other piece of this exercise was about creating tolerance in the rider and the horse. By committing to doing the pattern that set number of times, and not worrying about quality (though it always got better), the horse learned to show up and accept the ride she was given and to continue to have to listen to her rider who was giving her lots to think about with those frequent, but predictable transitions. In other words, and psychologically important, the tense horse didn’t get to bail out on the job or the training just because she was tense. Both sides need to learn to not take the horse’s tension personally.
IMO, people and horses have to learn how to work despite tension. And you don’t teach the skill of mentally hanging in there even during confusion without putting a horse into that spot and then helping him to find peace.
Now, I’m a very old hunter princess. I know how to will my mind and body to go slowly and softly even if we have a long gallop to a single oxer where every fiber of your being says to start picking at the horse until you see a distance. Really, my job is to Do Nothing, and that is skill you have to learn. So I can and have tried giving tense horses the super chilly ride I learned how to do in hunter world. That works for some of them-- the ones that are not smart, less scared (and more secure if a little mentally lazy) or more dull than the “teacher’s pet/herding-dog-smart” horse like the OP’s gelding. As my mare taught me, that kind of tactful ride felt like abandonment. In other words, when she got worried, my impassive quietness seemed very much not in her experience, so she felt she had better stay on guard as the alpha mare who was left alone to take care of herself; I was no help and thus part of her problem rather than the source of a solution.
I love the techniques described here for teaching the horse’s small, immediate terms of praise that mean something to them. The “yes” for a single good step and a way to call the horses attention to what he did right is fabulous! But also or before that, IMO, you have to teach the tense horse how to “stay in conversation” with you–that you will intervene in his world and that the more he listens intently to your aids, the more predictable his world will become. He has to learn to find peace by taking his sharp mind, huge work ethic and sensitivity about his well-being and how he’ll survive in your herd of two, if he applies himself mentally to you.