I don't think the humor is in the non-answer, I think the humor is in the fact that we're introduced to a person who demonstrates what is apparently rational, goal seeking behavior, and then proceeds to ask for something he doesn't want and has no reason to want.
I also think part of the insight is that by the time he has the other two things, it doesn't really matter what he has for a head.
Speaking of things that are funny to some and not others, an instructive example is the Orange Head joke. Usually when it's told, the audience is sharply divided into those who think it's hilarious and those who struggle to see what's funny.
Here's the Orange Head joke:
Do you think it's funny?
If you search for this joke's key words, you'll see many pages where, after it's told, people react incredulously and ask where the joke was. Others at the same time are laughing their heads off. Here's a blog post that attempts to analyze this, though it doesn't get far.
(I personally think it's hilarious, and easily the best joke I heard last year. When I retold it at my blog, I got many concurring comments, but also comments from people who didn't see anything funny, even after those who did tried to explain what they found in it. Several people went on to convince themselves it's garbled and there must be an "original" version in which the final remark makes sense and is funny - and offered several ideas of how it might go).