I am not a hypnobabies expert, but I did use hypnobabies with my first and I'm practicing for my next birth in a few weeks.
First, during pushing I have to say I wasn't very focused on the technicality of where my switch was because the experience was very intense, but I think it was in center. Pushing and crowning were basically painless for me, just hard work. I had a hypnobabies doula and listened to the pushing track. I remember my doula reminding me to guide the anesthesia and let the baby's head bring anesthesia with it.
I feel like I underutilized my center switch during my birth--practicing hypnosis during the last month was very hard due to RLS and severe sleep deprivation--but one thing I get from listening to the materials this time is the notion that you should do what feels good to you in the moment, even while you're practicing with the tracks and especially during birth. This time around, I use the center switch for a lot of my hypnosis practice because being told to stay still sometimes triggers RLS for me, and the anesthesia was super effective when I tried it on my temporary but very painful back injury.
I plan on using my center switch a lot more in this upcoming birth because last time I didn't interact very much with my lovely birth team or my husband, and I'd like to enjoy and bask in their presence a little more. There comes a time in birthing when I will want to go completely inward, and at that point maybe I'll use the off switch much more during waves.
Hope this helps a little. I wish I had been less of a rule follower my first time around with hypnobabies. It is really a flexible method even though the materials don't necessarily present it that way. The goal of hypnobabies is to make birth enjoyable, and I kind of missed that last time. I had a very nice birth, but I was so focused on success that I didn't enjoy the process enough. I wondered when I got pregnant again if this was a flaw of hypnobabies. After going through the materials again, I feel it might tend to make people too goal oriented or task oriented, but being aware of that, I am overriding that and just looking forward to the beautiful experience.