Z2IO located at existing control module.
Disconnect the 2 existing low voltage wires at the control module side.
Wire relay on the Z2IO to the existing contacts the two low volt wires were connected to.

At this point you have control over the fireplace via C4 KP button link located elsewhere, fireplace timer experience driver, custom button, etc.

If you want to maintain the toggle functionality of the existing wall switch...
Leave it wired as it is at the switch side.
Connect the other ends (previously removed from above) to a contact on the Z2IO.
This will give you the ability to bind the contact up to program against for toggle on/off of the fireplace from the existing switch.