I have only begun to delve into this phenomenon. For sake of this debate, let's keep this limited to ONLY the case for Apollo 14 where the flag moves 8 times while the astronauts are inside.
As my thesis, I'll show the surely-famous clip from Jet Wintzer.
https://youtu.be/p_66cqMQsW4He seems to do a good job with this presentation, but I'm guessing it's flawed.
I've also read some debunking that suggests it was the result of "cabin depressurization" where the air was expelled close enough to move the flag.
However, I've not seen the proof of alignment of the Flight Journal aligned to these cases of flag motion to prove a feasible correlation.
Nor am I aware of any explanation for what would explain how force is PULLING the flag towards the LEM? For the majority of the time, this flag is offscreen, suggesting that it's "resting state" is offscreen to the right. And then some force PULLS it onto the screen, towards the LEM.
How do PNA's explain this motion?
(PNA = Pro-Nasa-Advocate -- is there a better term to use here. I assume my acronym here is HB - Hoax Believer)