The thermopile in your fireplace puts out millivolts nothing near the 120v the light switch was designed for.
Gas fireplace switch wiring.
If this is the case there will be no power to run the smart switch unless it is battery powered.
It s probably just a matter of finding a switch with a low enough on resistance.
It shows the parts of the circuit as streamlined shapes and also the power and signal links in between the devices.
When attempting to automate a fireplace with a smart switch you have a problem because a lot of switches require a neutral wire to be connected so they have constant power for the zwave radios to send and receive signals.
Crimp the connectors securely to the wires.
All the switch is doing is making or breaking a connection it is not wired up to standard 110 volts.
A generic low voltage switch from a electronics store or ripped out of a toy would probably do it for example a 12v spst.
A wiring diagram is a simplified traditional pictorial representation of an electric circuit.
On the gas fireplaces i have installed the on off switch was a millivolt contact.
Assortment of gas fireplace wiring diagram.