Ok, I got it working after some fiddling! So it seems the forticlient installer will not work if it thinks forticlient is already installed - even if the application files are corrupt or if they have been systematically deleted.
Likewise the forticlient uninstaller will not work if the Forticlient application does not exist. This means users are stuck in a catch-22 if their installation gets corrupted. They can't Uninstall because the Uninstaller doesn't think it is installed. It can't reinstall because the Installer thinks it's already installed and will only allow updates. So no way backwards and no way forwards.
I think this can and should be improved upon on FortiClient's side. The Uninstaller should work even if not all the pieces are there, The Installer should allow a user to install even if it thinks the Application is already installed.
The only reason I was able to get out of this situation is because my Time Machine backup had the FortiClient program and the FortiClientUninstaller still stored under the Applications folder from an old backup. I was able to bring these files back. The FortiClient Application itself would not run - just showed a white screen, but bringing it back at least made the Uninstaller run which then made a fresh install possible.
So, problem solved for me. But if I had file corruption and no backups, from what I can tell there would be no way out of the problem!