I think this is reverse psychology of sorts . . . but if we have a shy or hard to catch goat (or calf or horse . . .) we leave a leash on them at all times. They aren't tied to anything, the loose end just drags on the ground: its usually only about 5 or 6 ft long, but all we have to do is walk up quietly and step on the leash. After the first couple of times, they realize that they are caught and quit trying to escape.
You'd think they'd learn to run away from you and keep a larger flight zone, but the opposite is true. First they learn there is no escape, then they learn to be comfortable with you in their presence.
For larger cows (that could take me, leash and all for a "sleigh ride"), we lasso/halter/leash them, and tie them to a stout post for an hour so they learn they can't beat the rope. Once they calm down, we get out the horse brushes and spend 20 minutes or so brushing them, combing the mud out of their coat, and talking gently to them. We start at the SHOULDERS to keep away from the back legs so we don't get kicked, but it doesn't take long until they start to like it and gentle down. Once they are calm, we brush them over their entire body. Some like belly rubs more than others! Repeat daily or as often as able, leaving the leash on them so they're easy to catch and don't learn to run away. This is how we "domesticated" a pair of 600 lb heifers. Even today, I can walk up to them in the field and touch them. Because they are so calm, and because they are now my herd queens, the entire herd will let me walk within 5 or 10 feet of them to give them a close lookover.
Yep, we tried graining the heifers to encourage them to gain our trust, but we got LOTS more mileage out of a simple horse brush. Try it!
