I'm not sure I understand- we do a lot of giving to pressure (pick up on the rein and he immediately turns to touch my foot with his nose), but I'm unsure if that's what you meant, since his head doesn't stay perpendicular to the ground during that, it does twist so he can stretch further.
yeah, moving this way will create a bend only in the neck, as teh hrose twists the head to the side and reaches around primarily by bending the neck. They do this to scratch a fly bit on their own shoulder, or even flank. amazing how far back they can reach.
Im not a big fan of static 'suppling' like that. It doesn't do much for suppling the horse in either the poll or the hind end, and can create a horse that is 'rubber necked', meaning he can and will bend sharply to one side to avoid contact of the rein, and the neck 'breaks' from the body, like a semi truck jack knifing, and the horse can be bent harsh to one side, while still running smack through his outside shoulder, forward or sideways AWAY from the direction you are asking him to bend.
And, if the horse is standing, that severe , twisting bend dumps the horse onto its outside shoulder and does nothing to connect the rein contact to his hind feet.
You want that soft, tucking of the horse's jaw into his own neck, as he just swivels slightly to each side, softly. And if you ask a bit more, he should lift his whole neck, poll going higher NOT back toward you, nor him tucking lower, like taking his chin to his chest to go behind the rein. And if you take a little more rein, the horse should slightly rock back, as he is getting ready IN HIS BACK FEET to move off to the direction you are asking , since you will be having a bit of a bend to one side, you will have that rein a bit shorter, getting the hrose to think in that direction, in mind, mouth, poll and hind legs.
sorry if this sounds a bit woo-woo. it's much easier to show than to tell.