By any chance, is your user account defined in a network-based authentication database, like NIS or LDAP?
Yes, exactly so, it's defined by NIS. The machine where gdm login is failing is an NIS client bound to a different Debian machine (still on Debian stretch) which acts as the NIS server. On a related note, my home directory is served by NFS from the same server to this client. (I've been managing a home cluster of Linux and some other UNIXes like this for decades.) I assumed everything was working correctly with this since I can log in to the client host via ssh and at the console. --Ken