OP, is your coach thinking of a light seat like the big show jumping & equitation riders do? I had a similar problem, where my coach was always telling me to be “lighter.” I can’t remember what made it click, but eventually I realized that she wanted a much more open, upright position than I was used to.
I tended to either go low and forward in a proper galloping position, or I’d sit super deep and drop my shoulders back and drive. I found that thinking about basically standing straight up helped a lot. At first I had a hell of a time trying to stay in that spot. It felt super awkward to stay up without any help from my seat or my seat, and if I went much lower than just plain standing, I’d pretty much topple back into that deep seat.
I ended up doing a lot of, like, holding the stand for a minute, then dropping, or holding for one side of the arena but letting myself sit around turns. I still struggle with it if I’m getting tired or freaked out, but it has gotten a lot easier to control and to sit softly without unnecessary whomping.
A big thing that helped me learn to hold the lighter seat was just doing dryland drills in the gym. It takes some weird muscles that I really wasn’t used to using, and the balance felt really different for a while. I ended up doing a lot of squats, using weight machines for certain muscles, and practicing controlling the deepness of my two-point on a balance board.
Another thing that might be screwing you up is just your horse’s confidence in your position. I haven’t trained a horse out of this, but I have met some in the past who’d sort of been taught (accidentally or on purpose) to wait for that driving seat cue. It sounds like you’ve done most of the training on him, and maybe he’s just a bit thrown off by the new cues and unsure of how he’s supposed to respond.