My 19-year-old horse is 95% blind, and when he's not eating or sleeping he walks in circles. What can I do to stop or minimize this behavior?

You certainly would want to have this horse evaluated by a veterinarian to be sure he can walk in a straight line, and to get an opinion on why he is blind and on what his quality of life might be from here on. Your veterinarian might even want to refer you to a neurology specialist. That person could offer an opinion on whether the horse could go on safely, and alert you to the special care that a visually impaired animal requires.

Then if the decision is to go on, I would first try a companion animal. Some disabled horses bond and can learn to depend upon a companion as if it were a "guide" companion. The blind horse might come to follow the companion and feel some socially facilitated "calm" that the buddy will be vigilant to danger. I would try to find a kind, submissive pony or a donkey. It could take some trial and error to find a good match. If the circling is not incessant or causing harm to the horse, I would let it go on and try to think of it as exercise, just in a small area that perhaps is perceived by the horse as a "safe" zone where it will not run into objects or surprises. But if it is at a harmful level, for example causing foot problems, excess energy loss, or the animal seems anxious when circling, you might try safe tethering or a tie stall for a few hours a day. It might sound cruel, but actually I have seen animals settle down and seem much more comfortable, as if the tie stall were a secure place.