There are different philosophies on how to handle going behind the vertical, and to me it depends on whether or not the horse is actually going behind the bit or not. My violent bucker used to be afraid of contact and duck behind the bit. I was encouraged here and by some people in person to always keep contact with him. In his case, that would make it even easier for him to tuck further and leave me with no control of bucking.
In his case, we had to go very up and very open. Because open inversion was against his nature / build, he preferred to reach into contact from there to being held so open. Bonus of he never could tuck and avoid the bit from up there, so it was easier to stay on. It also ensures the bit only works on the corners of the mouth as it should, so he started to learn to trust contact more with his tongue and bars never having pressure.
My mom’s mare is the type of straightforward horse who is always looking for the simplest answer, and whatever is easiest for her. We suspect she was ridden in draw reins at some point, so she would pose behind the vertical without really using her body and just cruise along pleasantly. With her, I maintained contact where she was and asked her to use her hind end more. Lateral bending (first just large circles) to interrupt her efforts to pose and never letting her escape contact by posing taught her it was actually easier and more comfortable to swing through her topline. I of course allowed when she wanted to reach into the contact and open up. Fixing her was a matter of weeks vs years for my gelding with his “issues.”
What a longer rein can do for you, if it’s a horse who is afraid of contact, is allow the horse to build muscling to hold itself more open and therefore encourage that kind of carriage. I prefer the other methods, or what we did with my gelding which was the use of two reins, one on a noseband and one on the snaffle, so he had contact but on his nose instead of mouth.
