Prince & George

Today I rode two horses, my first day helping Mike, Prince and George. (Two chestnuts - then Willig, who I swear was jealously watching me and hence, well behaved when I finally got on him.)
Prince is young (4?) and seems to have the personality of his mother. He was very mellow for a youngster. He acted like I expect warmbloods to act. A flick of the ears rather than a rapid sideways skittering.
George is a bit more frisky, but thanks to the few years now of working with Willig, it wasn't a big deal (!!). The only thing he did (that I forgot to ask Mike about) was when he was trying to do a racecar canter, and I'd ask him for a down transition, he'd do a collected canter instead. So I obviously don't know the distinction between those two aids, and should figure it out so I don't confuse him in the future.
Both of them, like Mardi, Charlie, and Pablo, were much more "rolly" and easy to ride. I was thinking it was because Willig is very narrow compared to them, but then, as I thought about their confirmations, I realized that couldn't be it (they all have very different confirmations, and Willig's is actually, while narrow, quite elegant).
And then I had an "ah-ha" moment. It's their balance. Their hindquarters are engaged while Willig still spends a lot of time heavy on the forehand. It's what makes them feel like a wave rolling from back to front (it comes under the hip bone, lifts it up, and gently lets it back down), makes them easier to sit the trot on, and makes them easier to ride in general.
I feel like I'm on the verge of "getting it", but I really, really want to know how to create that engagement myself. I will NEVER EVER go back once I've figured that out. (Although I have no idea how I've ridden so many horses - 100? - and never felt it until this barn.)
As an aside - the trampoline seat is really coming along. (That's what I think is the verge of getting it. Suddenly, I can do trampoline seat no problem.)