Do you need a free hand to hold the Mirror of Guarding Reflections or could you just strap it to your forearm?
Mirror of Guarding Reflections:
Reflections visible in this palm-sized hand mirror always seem ghostly and insubstantial. When a creature holding the mirror is targeted by an attack , he can spend an immediate action to summon his reflection from the glass to interpose itself between him and the blow.
The reflection functions as an image produced by the spell mirror image. If the image is struck by the attack, it shatters with a resounding crash. The creature that destroyed the image is subject to bad luck; the next time it makes an attack roll or saving throw, it must roll twice and take the worse result. If the attack does not strike the image, the image fades away at the start of the mirror bearer's next turn. The mirror can be used three times per day.
Cost 7000 gp, item from ultimate equipment, emphasis mine
The reflection functions as an image produced by the spell mirror image. If the image is struck by the attack, it shatters with a resounding crash. The creature that destroyed the image is subject to bad luck; the next time it makes an attack roll or saving throw, it must roll twice and take the worse result. If the attack does not strike the image, the image fades away at the start of the mirror bearer's next turn. The mirror can be used three times per day.
Cost 7000 gp, item from ultimate equipment, emphasis mine
It specifies holding the mirror. That pretty clearly implies using your hand.
P. S.
The item already is slotless. I’d like to use it for my TWF. Due to this I really couldn’t spare a free hand for this item.
In case I’d actually need to hold it in a hand, what would be the cost upgrade to turn it into a brooch, ioun stone or other hands free item?
ninjaed, so no P. S. but a normal follow up question :-)
It's technically slotless so there would be no price change.
Definitely an ask your GM situation.