SysAdmin account shows at login, but doesn't work and is not listed in Users & Groups
YES !!!! 
I got it. I used Directory Services.

Full details are here: https://support.apple.com/en-us/HT203513

I summarise below, in the unlikely case the link disappears:


Log in with a user account you want to keep.
Press Command-Space to open Spotlight. 
Type Directory Utility and press Return.
If the lock  in the lower-left corner of the Directory Utility window is closed, click it and enter an admin user's name and password.
Click Directory Editor in the Directory Utility window's toolbar.
Choose Users from the Viewing pop-up menu.
From the list on the left side of the Directory Utility window, select the user that you want to remove. The name you select should be identical to the name shown in the Users &amp; Groups pane of System Preferences when that user is logged in.
Click “-“ in the lower-left corner of the Directory Utility window.
Verify that the selected user is the one that you want to be removed, then click the Delete button.


After you remove the user account, you can delete its folder:


In the menu bar, choose Go > Go to Folder, type /Users, and then press Return.
Drag the folder for the account you just removed into the Trash.
Choose Finder > Empty Trash to delete the folder and its contents.


Problem solved.