Ok. As it stands now, I have only the "case 1" fstab entry in place, and
after this line of the backup script:
cd /media/ExternalHD/Backups
I've added these lines:
if [ "$?" = "1" ]; then
mount /media/ExternalHD
cd /media/ExternalHD/Backups
fi
which (at least in theory) should mount the external drive if it's
connected but not mounted.
(And if it doesn't mount, then the backup gets built in the home
directory instead, which is no big deal, since it's backing up something
from a separate physical box.)
Tonight, I'll leave ExternalHD connected but unmounted, and tomorrow
morning, I'll see what will have happened.
Thanks.