So far, so good. Well, almost. I copied Pictures folder (700 GB) to the second external drive, and have the Time Machine back it up, in addition to the internal computer.
However, that new, second external drive is occasionally showing 0 items, 1.3 TB free (obviously, there are 700 GB used, so it shouldn't show 0 items). The first time it happened, I ejected it and reconnected it, and it properly showed the full directory of the Pictures folder.
Does anyone know why is this happening?