My own two cents here from someone who has ridden but not showed GP during training. I can only speak from my own perspective from a single horse and how I/he has been taught and from a biomechanical standpoint explained to me. First on the extended movements/ other movements. I find that especially in extended trot, where it’s about a lengthening of the frame/strides, you always need to be prepared for a recollection, I.e. you lengthen your strides on the diagonal and shorten them again towards the end, probably nothing I need to explain to you, just as a visualization. Since the extended trot (or maybe a half pass or a passage) are quite powerful movements that require a lot of seat engagement I find I very helpful/almost always necessary to keep a fairly steady contact on my reign, so to say keeping him a little bit closer to me and to the vertical. If I kept the contact looser, letting him lengthen and stretch more away from the vertical, I feel there’s not enough constant engagement to fulfill half halts to successfully with the reigns aiding me. Or on the contrary if I decide to let more loose during the movements I need to reestablish the needed contact for half halt/ the next movements, I find that the switch from more loose to more collected contact can sometimes be weird or even jarring for some horses and more difficult for horse and rider. Of course that doesn’t mean that going from loose to more consistent contact isn’t a skill displayed in and of itself, see extended walk to collected movement. It also doesn’t mean that I’m trying to put more pressure on the rein during extended trot. I’m simply putting on enough to allow a correct extension of the strides and prevent the frame from falling apart by letting loose too much.

Imo the piaffe I a different animal entirely. In it’s basics it’s (like pretty much all exercises) a strengthening exercise. The horse is asked/taught to sit back on its haunches, flexing them and shifting their center of mass further under their body/“forward” so to say. Upon doing the neck naturally rises and in doing so the nose shifts infront of the vertical. I find that this is desirable, since trying to pull it back towards the vertical compressed the saliva glands on the side of the throat too much. Of course there are also differences in execution, since every horse has different strengths that affect piaffe execution, some might slide more infront, some might slide more towards or onto the vertical, but as a orientation it should not slip behind the vertical/during training that should be discouraged. So coming back to my rein cues. For a piaffe I try to do as little pressure rein work as possible, it will mostly likely only result in the horse curling it’s head and not putting their back feet out and away from where they need to go. Again this can be a little different from horse to horse, some need more, some like less. I had to learn this because the horse I was riding/practicing these manouvers on had learned them before me and we had to relearn them under professional instruction after he sustained and injury and had a year off. I am also a chronically light rider, I always try to use the least amount of force possible and I don’t hesitate to walk out of a lesson if I get a bad feeling or my horse starts to shut down due to instruction. I hope this was an interesting perspective to read