yes
Yup, unarmed strikes are light weapons too.
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That you can TWF with unarmed strikes (because you can punch with your left and right arms) but you can't, four, five, six, etc. fight (because you could presumably also be hitting people with your knees, feet, elbows, forehead, etc.) is one of the reasons that there's a distinction between "your actual hands" and "you've only got two hands of effort" in Pathfinder.
Of course, that would arise the same way because someone can strap on a boulder helmet, a boot blade, armor spikes, and wield two kukris and they still can only make two attacks* when TWFing.
So I think the point of the rules is that the two-weapon fighting full-round action entitles you to take an additional attack with whatever weapon you haven't already used, no matter how many weapons you have. So there's no real difference between "letting someone use the dagger in their left hand after they used the dagger in their right hand" and "letting someone punch with their left arm after they punched with their right arm" so the rules should reflect this.
*at, say, level 4.
The point of TWF is "when you make an extra attack"
Your main attack and iteratives take primary penalties.
The extra attack gets "offhand" penalties.
Humans UAS are light weapons.