Thanks for the advice, guys. What I was looking for, however, was a way to do the favicon in a way that would be internal to the HTML file itself. The reason for that is that my Tiddly Wiki is stored on and accessed from my own local drive, and I would have preferred a way to reference the icon file there, too. That was problematic.
However, I did find a solution.
Favicon.cc allows users to create the favicon itself (no great trick, I suppose, since you could do pretty much the same with MS Paint and some patience. But then you have the option to store native HTML code which can be implanted into the Tiddly Wiki pre-head markup shadow tiddler (I know that none of that makes sense to non Tiddly Wiki users; you’d have to check out Tiddly Wikis.
Anyway, I’ve got the favicon working fine now. Thanks again for the tips.