"Show Keyboard Viewer" and "Show Emoji & Symbols" not working

The Hide and Show commands for Keyboard Viewer and Emoji & Symbols are not working on my 2012 MBP (Mojave 10.14.6). The icon is in the menu bar, but nothing happens when I click on the commands, other than "Show" becoming "Hide", as would happen if the viewers were in fact working.

I removed the following from my Library/Preferences folder:

com.apple.keyboard.plist

com.apple.keyboardservicesd.plist

com.apple.KeyboardViewer.plist

which had no effect. They were not regenerated on re-booting (which may be a clue), and I've put them back. The only other clues are that the icon in the menu bar is generic-looking, and not the flag indicating a US keyboard layout (which I have set), and that the problem persists when logged in on a Guest account.

Anybody have any ideas about how to get it working again? I depend on this feature to get Greek letters for my technical writing.