Looking at it closely you can see the flag moves slight away from the astronaut at the momentof him passing by it.
That's the precursor motion we're debating. It's not clear it's actually occurring. Others see it; others don't. That's one of the questions that a detailed analysis would have to answer.
Then as you mentioned it springs back and oscillates mildly.
It's not clear (based on the uncertainty above) whether the motion toward the astronaut is the first observed motion or a subsequent.
If it was electrostatic what sort of interaction would we expect to let this happen?
I'm not sure what exactly you're asking.
Can the force needed to cause such a movement be measured?
Yes. A better question is whether I can measure it with the tools at my disposal. Not really. Not with any confidence.
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