Third Broken Thing
This is one of those times when calling on other 996tt owners helped diagnose the problem. I posted the video and asked the 996tt forum on Rennlist for advice. Armed with the suggestion that it was the "window regulator," I then went to YouTube. Where, lo and behold, there were several videos (gathered here) that confirmed the diagnosis and provided a nearly complete step-by-step tutorial on how to fix it.
In the end, I opted to get it fixed, rather than doing it myself (mostly because I didn't want to mess with the delicate adjustments necessary to get the window to shut cleanly). But it was nice to know I probably could have done it myself, if I needed to. The new regulator was about $200. That, plus 1.6 hours of labor at SF Porsche-specialist The Stable, and all was well again. Total cost = $468.