well, my trainer will ask the horse , by a small vibration on the lead line, to look at her. If horse ignors that, she will give the leadline a good solid toss up against the horse's under jaw or neck. Or, a firmer yank. It is not so much what the movement is, it's just that it will interrupt the hrose's outward thoughts. The horse may raise its' head straight up. Don't worry, just give it a second to look at you and maybe lower it's head. If it looks right, give it a bump with the lead line to bump it back to the left (center), and the opposite if it looks the other way. Make looking elsewhere uncomfortable, but leave the middle a place where you will give it a minute to look at you, and it may lower its head.
The desired reaction is that the hrose will look "right down the line" of your leadline at you , at the end, gving you two eye, two ears, and in that state, you can encourage (not pull, encourage with a little feel on the line) that the hrose lower her head and look at you without "giraffing". Now, you've GOT her mind. Go take it somewhere. Start walking along, leading her , going varied directions and speeds and getting her to do so well. Keep in mind that she should be brought back to looking at you whenever she tries to look off to that other horse, and certainly when she calls to that horse.