The mare I just had was 16.1 and hated her head touched as well.
Something I was taught to do, was work with him/her in a roundpen first. I was told its also a "join-up" activity. I wouldn't know, I don't know much about that area.
But stand at their shoulder, facing the same way they are, your body facing forward towards their head. I had put her on just a long cotton lounge line, and just let it fall to the ground and laid out, so A) you don't have to try to hold them as well and B) if they spook or try to get away, all you have to do is grab it. And its long enough and laid out so if they are to get tangled they can get out of it without harm.
(Which I was told is also a good thing to do with horses, because if you want them to get used to things on/around their feet & legs. And also will desensitize them if for any reason you need to put hobbles on them or something
Raise your right hand up (or do the opposite if you are leg handed) and put it right behind their ears, right behind their poll. And don't "press down" per say, but put pressure on the area.
She freaked out at first, and didn't like it, but once she lowered her head to the ground, I let up. Then gave her a minute to process what I just did, and that I let go after she responded.
Do this again & again & again & again. Its all repitition. The more I did it, she realized that when she put her head down I let up, so she'd keep her head down longer so I wouldn't do it again.
It worked GREAT for when I went to bridle her and halter her after that. MUCH easier.
Hope it helps/works for you!