[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.