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.