Bearded blade and armor spikes use your metaphysical off-hand.
Yes, I am very aware. My point is the TWF has nothing to do with hands.
You can use two weapons without TWF.
You can use TWF with your hands on a Two Handed Weapon that you don't use in that round.
TWF does not follow many, many of the "normal" rules for penalties.
TWF is a unique subsystem within the rules that is VERY hard to understand if you start linking your understanding of it to how many weapons or hands you are using. Neither one matters. It can only be understood and based on how many ATTACKS you make and how much EFFORT each of those attacks require.