OP, I know what you’re saying. However, I’m not sure how to evaluate this mind “long distance” aside from really trusting the seller’s opinion.
I like a horse with a sharp mind, and a good filter. They are confident in themselves, so they are able to focus on you and your requests, and easily develop a connection. I love these horses. They are perceptive, quickly make positive associations, and have a good memory for exactly what they did to obtain a reward. They think on a higher plane than an average horse; they process and make conscious decisions instead of merely reacting. They are trainable, yes; but in a more complex way.
For example: my late advanced mare was amazing at opening gates for me. I didn’t have to cue her specifically “over to the left, stand still, pivot right, back up 3 steps…” etc. I just walked her up to it, reached out with my arm, and she maneuvered herself so i could reach the latch. She would stand patiently as I leaned, struggled with a rusty broken gate, and when I was ready moved deliberately to help me open it. I didn’t really “train” her to do these steps…but she knew going through gates was necessary to go out and ride home, and I was an active teammate in the process. She was extremely intelligent in other ways, but this was most obvious. Interestingly, her colt was exactly the same way, from his second day under saddle.