I have been learning wing, and I humbly suggest that the "wing pump" flap might be being taught incorrectly. I think this intuitively comes with time to advanced riders that there is a timing element, but not particularly helpful to beginners? Maybe it is taught this way to simplify things? I don't know but would be interested to hear some thoughts on this. Intention with this thread is to help progress things, and is based on observation.
Here is my analysis, take this with a pinch of salt. This is based on what I've seen, and then experienced riding a downwind board with an Axis 1300 and managing to start in ~10-12kn.
The wing pump is described as a circular "pullup" motion, but places no emphasis on moving the wing through the air. While actually the desired movement is much more subtle than just ripping the wing round in circles:
1. It's a circle movement, but
viewed from above at 45deg angle,
not the side
2. It's a well timed accelerating woosh forward and up, not a manic circle
3. It feels like you are pushing the wing forward in a scooping motion, with your back hand doing the work
4. The hands don't move in sync, one goes just before the other

Here are some examples from the wild (non instructional) and all seem to do something like what I've tried to describe:
www.instagram.com/p/CkqqtE-oLjf/Clear at around 0:30 (instructional video but describes more the foil pump)
Instrucional:
These 4 videos all describe this very circular "pullup" technique, what is interesting is that the Duotone video describes the pullup technique, but then the rider when viewed from the top does exactly the whoosh forward that I'm describing with the forward push at 2:00
Gif works here:
makeagif.com/i/AsTR0R
1:40
2:50
Disclaimer - I didn't exhaustively search for instructional videos, just the top 4 youtube results which all seemed to describe this very simple movement, which doesn't really seem to work for me, and then watching light wind videos, I see people do something entirely different, and similar to what I felt intuitively. I also had a lesson but I don't think it covered pumping the wing that much.