I know this is going to sound really unhelpful... but just put the head down when he puts it up. And don't just try, do it! You don't need a fancy bit or any contraption, just a bit more will than him. If you have to, bring him back to walk, take the head down and go back to trot, bit make sure you are maintaining a connection and not just letting him go for a cruise. Eventually you will be able to correct him with less aid and in the trot. A circle might also help you. To get the head down I would plant my knuckles of one hand on the neck, and without pulling back, raise or open the other rein and encourage him to flex laterally. You also have to remember that the leg goes to the hand, so put it on! This usually results in "give" longitudinally too and when the head drops, reward.
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Sounds good in theory, and in the school I'd be more willing to give it a go, but I know a lot of horses, and from experience, that if you try and put them in a forced headseat become extremely strong, and there was some tanking involved.
I prefer having a martingale on hacking, to use as a neck strap in case things go wrong.
If it were me, I wouldn't be trying to put him in the headset if he's tossing his head up and hollowing his back, it may be a battle of the wills, but unless you pump some iron one that is more likely to frustrate and be a battle of strengths rather than wills- also OP what is your riding experience?
Not picking your post apart anebel, when I first started schooling Duffy she was like a giraffe, inside stayed on, outside hand give/take and legs ON, but different circumstances, and if the horse is doing this as a pre-empt to bolt, go, or is barn sour, is this going to be effective?