My workaround for a missing cursor *was* to go to the Login window and log back in. Always worked, for a while, but it had the side effect of closing down my VPN connection to work.
So, the workaround I stumbled on based on some thoughts in this thread, was to go to System Preferences > Accessibility, and turn on "Use scroll gesture with modifier keys to zoom". With that setting turned on, control-scroll wheeling to zoom my screen in and out brings the cursor back now.
This workaround's much easier, so thanks everybody for leading me there.
The update this morning to 10.8.1 didn't change anything about this bug, nor did the PRAM reset or Mountain Lion re-install that Apple Support had me doing.
Incidentally, Apple Support rep said my call was the first he'd had about this, so make sure you contact support so they can fix this.
Hope this helps someone.