[mft_]

It feels a little like Schrödinger's cat - if you contribute, you alter not just the direction and content of the meeting, but also the dynamic. By getting involved (opening the box) you would irrevocably alter what you observe.

If my goal was truly to observe the CEO and learn from him, my approach would be to be as silent and 'small' as possible - don't speak, don't draw attention to myself, sit behind the table, not at it, etc. I'd want everyone --including the CEO-- to forget I was even there.

I suggest you need to figure out what your goal truly is: to learn from him, or to 'bring value' for some reason? I'm not sure the two are compatible.

[realrali]

You make a good point. I think my need to bring value comes from being so grateful for the opportunity - I feel like I need to do something for him because he's doing something for me. I guess my time to 'repay' him will come later.

[crazypyro]

I would suggest keeping your contributions limited to 1-on-1 conversations with the CEO, preferably soon after a meeting.

Taking a role in meetings could potentially create a lot of awkward power dynamics between you and the other executives, in my opinion.

[eddieroger]

They're doing this /for/ you, not to get something /from/ you. Show your gratefulness by staying out of the way. Maybe bring donuts in the morning one day, something that doesn't impact the business. You're shadowing, not applying for a job.