Sitting at my 'remote' machine, I logged in and started a graphical user session via lightdm on tty7. I then logged in and started an additional graphical session as another user via lightdm on tty8. So, I had two graphical sessions running concurrently.
Sitting at my 'local' machine, in an unrelated graphical session there, as I wanted to access both remote sessions, I sshed in to the remote machine and started, for each of the two users, an x11vnc server. I then started two x11vnc clients locally.
However, only one of the local x11vnc client windows showed a remote desktop; the other window was black (blank). The remote desktop shown was the one (F7) that was currently being displayed on the remote machine's monitor. I walked over to the remote machine and switched the display to the other user session (Ctrl+Alt+F8), causing that session to be displayed on the monitor there instead. As I anticipated, as the immediate result, the local situation was reversed: the local x11vnc client window that had been showing the remote desktop turned black and the one that had been black showed the other user's desktop.
How can I locally switch back and forth between remote sessions running concurrently? Is there a way to send a Ctrl+Alt+Fx to the remote machine (in writing this, I accidentally, locally, in the x11vnc client window (by pressing Ctrl then Alt then F8), brought up a pop-up with a menu of items, two of which were respectively labelled 'Send ctrl-alt-del' and 'Send F8'))?