This works, but is not very satisfactory - I can't expect the user to memorise all this!
- Right-click on an area of the system tray which is for some reason, empty. (Side note: I think this is part of the problem - not all applets are appearing, or appearing properly, in the system tray.)
- Choose "System tray settings"
- Choose the second settings panel, called "Entries"
- Set the Keyboard Layout visibility dropdown to "Hidden"
- Click the Apply button
- Set the Keyboard Layout visibility dropdown to "Shown"
- Click the OK button