Update: I've gotten the related topics control to work again, but it's not clean. 
Here's the deal. There are two necessary elements that are not appearing in the RH8 topics. The first, as Rick pointed out, was the id="RelatedTopics" bit. The second missing piece was a chunk of code at the end of the topic, something like:
<?rh-script_start ?><script type="text/javascript" language="JavaScript1.2">//<![CDATA[
if( typeof( InitEffects ) != \'function\' ) InitEffects = new Function();
InitEffects(\'a1\');
//]]></script><?rh-script_end ?>
...where 'a1' is the id of the button I used to access the hidden RelatedTopics control. The button (a1) lives in the template, er, master page (I *must* get used to the new terminology!) header, and the InitEffects code isn't getting carried over to the topic. Unless I include that part (and the missing id), clicking on the control generates an error. (Without the master page involvement, I apparently don't need to worry about the InitEffects part.)
Interestingly, the control needs the id="RelatedTopics" in two places. It does exist in the first spot, but is missing in the second instance. The same appears to be true of the SeeAlso and KeywordSearch controls, BTW. (Before I realized it was supposed to show up twice, in two separate but similar-looking instances, I was going crazy trying to figure out why it was staying and going and staying and going...
)
To make matters worse, editing the HTML code is only a transitory solution. As soon as I do anything in the WYSIWYG view for that topic, the HTML changes vanish. (I didn't have any success putting the script in the script box. If I did that, then RH didn't seem to understand that it needed to use that code.) So for the short term, I slapped together a script that adds in the missing bits. So to get output, I close the project, run the script, and then generate via command line. (I can also generate from the project, as long as I don't get into any topics that were altered.) If I need to use this solution for real production, I'll have to do a better script, one that will do a cleaner FAR. For now, while I'm testing, this is OK.
OK, so I have a workaround, and my Related Topics display and operate correctly. Hooray! The next problem is applying this solution to a RoboSource-Controlled project. Now THAT is worrisome. 
Rick, thanks for your assistance. I've got more work to do on this problem, but it can wait for a bit, I think.
G
I have submitted a bug report.
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