Here is my concern. I have the logo image along with the entire header section of the site in an 'included' file. How do I present that image in the image sitemap? Should I give the URL of the 'included' file that only contains part of each page and as such wouldn't make much sense to a user who would get it in a search result? Or is there another way of providing Google with the URL to that image?
How do I present that image in the image sitemap?
You probably don't need to at all. Why are you asking? It might provide some more context.
Should I give the URL of the 'included' file
No. Sitemaps are intended for indexing pages, not the individual bits that make them up.
The reason you're unclear where to add a reference to the logo is that the image extension tags are more intended for pointing out the "important" images in the page, which is generally going to be those in content, not your layout; the layout is just decoration for these purposes. (Else why not also add all your background images, arrows, etc?) Remember: this is for search engines, and they mostly don't care what your site looks like, just what the content is.
If you happen to have a page on your site that specifically provides things like brand assets, then do it there and include it in the image tags for that page. Some companies do this for press use, for example.
If this is important to you, then I'd probably just list it under the home page. I would not recommend including it for every page, just because it technically happens to appear on all of them. That'd be a waste of space and possibly trigger some alarms(that's speculative).
is there another way of providing Google with the URL to that image?
I'm not aware of anything "official" or widely-supported at this time.
But as a bit of trivia, I'll mention
Note that it's just an unofficial microformat proposal right now, not even a few months old yet. But if it's something you find interesting, you might implement it on your site(takes minimal effort) in support and maybe it'll take off over time.