How does Free-Hand work with Titan Mauler?

I am a small or medium Giant Instinct Barbarian with a large Free-Hand weapon, such as a large gauntlet. How does the Free-Hand trait work with the Titan Mauler ability?

The Titan Mauler ability states:

You can use a weapon built for a Large creature if you are Small or Medium (both normally and when raging). If you’re not Small or Medium, you can use a weapon built for a creature one size larger than you. You gain access to this larger weapon, of any weapon type otherwise available at character creation. It has the normal Price and Bulk for a weapon of its size. When wielding such a weapon in combat, increase your additional damage from Rage from 2 to 6, but you have the clumsy 1 condition because of the weapon’s unwieldy size. You can’t remove this clumsy condition or ignore its penalties by any means while wielding the weapon.

Whereas the Free-Hand trait states:

This weapon doesn’t take up your hand, usually because it is built into your armor. A free-hand weapon can’t be Disarmed. You can use the hand covered by your free-hand weapon to wield other items, perform manipulate actions, and so on. You can’t attack with a free-hand weapon if you’re wielding anything in that hand or otherwise using that hand. When you’re not wielding anything and not otherwise using the hand, you can use abilities that require you to have a hand free as well as those that require you to be wielding a weapon in that hand. Each of your hands can have only one free-hand weapon on it.

To my reading I never wield a Free-Hand weapon, I am just able to use abilities that require me to wield a weapon, but is Titan Mauler one such ability? The Titan Mauler doesn’t have a proper "requirements" entry like feats do because it is an Instinct Ability, but on the other hand it basically does nothing unless I wield a large weapon.

Moreover, when does a large Free-Hand weapon such as a gauntlet cause me to be clumsy?