After much digging and asking for help, a gentlemen passed on a link (below) that had the following information:
The session switcher will only show up if you have more than one
VALID session; a valid session is one that points to a valid
executable. By default in 12.10 you will have a session file for
gnome-shell, but gnome-shell won’t be installed, so the session is
invalid, leaving you with a single valid session (Ubuntu), and hence
no session selector!
I was very confused because, I know I had already run the Cinnamon install. But, this at least gave me a reason for the icon not to be there. So, I figured I would run the Cinnamon install again, despite having already run it twice. This time around, it began downloading even more files. I reset the computer and , surprise, the icon was there! It even had the GNOME options available too, despite the fact that the link suggested it wasn't installed...
So, I'm not sure exactly what happened. I can only assume that, while I was working on getting several drivers to run properly after the initial install, I must have messed something up.
Thanks for the help, everyone.