Thanks to some input from Terry and Trudie, I may be on the way to finding out just what the heck brown sauce is. It may be related to A1 in some way, but it's probably a closer relative to ketchup/catsup. Of course, now that I've spent (i.e. wasted) so much time on such a pointless question, I can't remember why I thought it was so important to begin with.

Here's the official vegemite web page. Don't get me started on vegemite; I've wondered what it tasted like for more years than I care to mention.