It is a multi-user setup with two accounts (mine and my wife's). My account has sudo access while hers doesn't. We each log in separately, and use fast user switching.
My thinking was that if I could set things up so that a non-admin user could not unmount the disk, then I'd prevent the accidental unmount of our time-machine backup disk.
One low-tech way of doing this would be to have a process startup when I log in that opens a file on the time machine (mounted) drive. That way, when my wife uses the machine under her account, if she accidentally tried to unmount the volume, MacOS would complain that there are open files on the drive and deny the unmount. Haven't tried this yet.
But I figure there must be a more direct way to require an admin account to unmount a volume. Is there?