How can I ask to shadow my boss?

So I work for a large non-profit and I am very curious to see what the guy at the top does. Not my immediate supervisor, I mean the guy at the top. I'm really not interested in the job itself, I'm just curious to see what he does, what his day-to-day is like. I would like to ask if I can job shadow, but I don't know how to do it, especially if I'm not really interested in the position itself. I can't imagine he would be responsive to a "just curious" approach, and I'm not sure that "just curious" even adequately explains my interest; I genuinely feel more than just curiosity. However, I don't want to lie and say that I am interested in doing what he does just to secure permission. I've been thinking about this for over a year and really don't know how to begin. Help.