Coming to my conclusions, I have realized why the show/hide links on the navigational templates only show sometimes.
Today, I was not logged in to my account, but was looking at a page. The templates on that page seemed to show as I was reading it this morning. When I decided to log in today and edit, however, those links disappeared. Curiously, I logged out to see if they would appear, and they did!
I suppose this would be the reason why I have not been seeing any show/hide links lately on the templates and why the Games template malfunctions the same way it did before. I have no idea what my login does, and it's not a MAJOR problem, but I've considered reporting it to Wikia, though I don't know if it's just me that has this problem.