Our impulse when working with our horses is often to shortcut the process of learning and just give them the answer, and demand that answer. Horses that resort to rote behaviors when you ask for something new, or who are nervous or reactive - Red was a very good example of this - are often those who have been forced into giving answers without any opportunity to learn, or horses who have been punished for trying and giving "wrong" answers. Horses like this have great difficulty in generalizing - in applying an answer they know to a related but not identical situation. This is a bit like a child who knows the answer to a specific math question, by having memorized it, but has no idea of the underlying principles, and who therefore can't solve a related problem - the child may know that 2 + 2 = 4, but can't figure out that 2 + 3 = 5, and so, when you ask them what 2 + 3 is, keep answering 2 + 2 = 4 - that's all they know how to do.
But allowing the horse the space and time to learn, and try, doesn't mean letting the horse flounder - it means giving them calm direction, without compelling them to a particular solution or making the "wrong" alternatives so difficult that there is no real choice.
But you have to know clearly what it is that you want - it can't be vague or non-specific - this isn't fair to the horse. It's also not just a matter of knowing the end goal - it's a matter of breaking it down into small steps that, one by one, as the chain of learning is built, lead the horse to the answer you want. You want your horse to discover the answer and be delighted with himself, and you too.
In order to be able to instantly reward the horse on each small step, patience is required. You may have to repeat the ask numerous times, and catch that exact moment when the horse says "you mean something like this?" - which may not be what you asked for but which is a tiny step in the correct direction. This means you - not the horse - you - have to pay attention - all the time - to the horse's interactions with you in response to your ask. If you do this, you will notice the very small tries - the steps on the road to the answer - that you want to reward. And, if you pay close attention to your horse, and are available to your horse so you can have a back-and-forth conversation, before you know it, your horse will be paying close attention to you. This is where connection and feel come from - it's not mechanics, it's communication and mutual attention. If your horse isn't paying attention to you, it's quite likely that you aren't holding up your end of the conversation either.
And remember that learning occurs all the time, not just when you're trying to train the horse to do something specific. The horse will be constantly asking you questions as you interact, both on the ground and when you're in the saddle. Always answer the horse's ask - the horse is looking for a conversation. If you fail to answer, the horse will either think that the whole thing doesn't really matter to you, or will fruitlessly fill the gap with behaviors in an attempt to get a response from you, or will do what the horse considers necessary to keep herself safe. This is where horses with poor ground manners come from - their prior handlers ignored their asks, probably because they didn't notice them, or because the handler had no clear idea in her own mind of what the horse should be doing - a vague "I want my horse to lead well" is of no use.
Never punish a "wrong" answer, or the horse's failure to understand what you want - just keep calmly and patiently asking, and guide/shape the horse's tries towards the right answer. Punishing a horse that offers a wrong answer in a try, or demanding that learning occur at a particular pace, is the quickest way to destroy trust and connection. Make sure you're never in a hurry - if you rush, things will take longer in the end and the learning will be contaminated with stress and anxiety.
Always keep in mind that if the horse can't or won't give the answer you want, you're likely to be a large part - or even the whole - of the problem.
If you're fair, and consistent, and calm, and clear, the horse will understand what you want and will learn to offer the answer you want, although there may be some wrong answers on the way - in fact, if there are no wrong answers, the horse isn't really learning and may be showing that he is afraid to try. And a horse that learns to give the answer you want with your guidance and assistance will develop trust in you and become more and more willing to try for you.
This is a virtuous circle - the more of this you do with your horse, the more secure and confident and willing to try the horse will be, and the more close your connection and understanding will become.