Jeb Boyd once told me that you don't need to know a ton of drills, but the ones that you do use you should know intimately and be able to use them in a variety of situations. The pivot slip is pretty versatile and you could whip it out for lots of students. I think one problem with it is that it kind of needs an outside set of eyes to tell the person doing it if they are doing it right or not. You could get pretty good at "doing it wrong" and not even know it. When I am using it with a student I always want to remind the student that nobody cares if they can do a pivot slip or not. I certainly don't care. The only thing that matters is if they are able to feel what I want them to feel in that moment and are able to bring it to their skiing. So things like edgiest or not, flexion-extension and so on don't matter unless there is someone scoring you (and maybe not then either).
I would contend a good pivot slip is slight aft on the skis on when ski are pointing across the hill, and very far forward on the skis when they are pointing down the hill.
From an external observer standing in the trees watching the skier pass by point of view, I would agree with this.
From the skier's frame of reference I would agree there is a fair amount of movement fore/aft however I would contend the movement results in the skier maintaining centered balance. When the skis are across the hill there is greater resistance so they will move back (uphill) to maintain their balance as you would when standing on a bus or train that is braking. As you turn the skis into the fall line that train will take off and you need to move with it in order to keep up and stay centered.
Also, from another point of view, being centered will often be considered aft!
As
@LiquidFeet describes, there is a bit going on. And as
@epic states, really easy to get good at doing it wrong!
Well that's clear as mud. There's a whole new term there - "vissage".
What does he say about that?
Eh, hard to paraphrase Joubert! Basically turning the upper and lower body against one another with consideration for resistance underfoot, use of the arms, effect of pole plant. So, counter rotation+
