As usual, I did some work, and forgot all about taking pictures that might help somebody else. Sorry. I have some kind of mental disability in that respect.
Anyway, this started with the need to replace the covers on both visor mirrors, which had long since broken off in the usual way.
I bought two non-lighted replacement mirrors on ebay (about $70/each), and did the repair as shown in this video:
https://www.youtube.com/watch?v=TGyJCpum6cE
(You can do this repair without removing the visors, or even removing the mirror units)
While doing this, I also found that the lights weren't working. I hadn't really noticed that before, since the covers were missing, and that would keep the lights turned off anyway. What was odd is that the lights still didn't work once the new covers were on. I checked the fuse box, but couldn't find any blown fuses, no could I find any fuse that actually listed those lights as on that fuse. So, I tested the bulbs -- all of them worked -- and tested that there was 12v and good ground to the lights -- there was. I came back to my computer and looked at some images of the inside of a new lighted visor mirror, and noticed that everything in mine seemed to be different. Looking at the picture below, which shows how all of the contacts should be, mine were wrong. The long brass bits that actually hold the bulbs and are the contacts were routed correctly, but the thing preventing the lights from working was the piece that the cover pushes against one of them to close the circuit. On both of my visors, the end of that clip was moved up above the little plastic post, as depicted in yellow, so that it couldn't contact the other part to close the circuit.
It's all sorted now, but I can't imagine any way this could have happened by accident. Can anybody think of a reason why a previous owner might have deliberately done it?
Also, if your mirror glass is pitted/old looking, it is very easy to swap the mirror glass out of the new units. There are four little plastic clips holding the glass in, and there will be a bit of glue/caulk on them too which just peels off. Be careful not to break the plastic clips on the unit you're keeping, but if you do, a bit of hot glue will work perfectly to keep the glass in place. You probably will want to use some hot glue anyway, in the way the original glue/caulk was used, to keep the mirror from being able to vibrate in the housing (at least, I think that's why it was on there).
By the way, if you just want to completely replace the lighted mirror housings, don't buy them on ebay. Currently, all of those are listed for $150+ each, but you can buy them directly from Porsche dealers, like Suncoast, for $99 each, and the Suncoast ones don't have the ugly decals on them!
https://www.********************************************** ******.com/product/EUROMIRROR.html
Well that's weird. Apparently, on this forum, you can't type s u n c o a s t p a r t s without it being changed to a long string of asterisks.