Just to add;If you get at least .400 DCMV between your two TP gas valve connections when the gas valve is not in the "on" position, then you should have enough power to run a thermostat circuit up to 20 ft. with 18 gu wire.
Take the red line off the gas valve TH connection and connect it to one of your two new thermostat lines.
Take your other thermostat line and connect it to the now empty TH connection on the gas valve.
This will allow the gas valve to be controlled by the thermostat while keeping the safety limit circuit intact.
Make sure all the wiring connections at the gas valve and the thermostat are tight and that your connection of the red wire to the stat wire is both tight & insulated against touching any grounding metal.
I've seen more then enough fireplaces just like the OPs that use a regular toggle switch. The wires and terminal plates on a plain Jane toggle switch corrode much sooner then the contacts. (a bit of filing and it's good as new)Mechanical stat is best.
Actually an old school mercury switch stat is best if you can still get one; the contacts of mechanical switches can oxidize over time, causing a voltage drop. It's insignificant on a 120v or even 24 circuit, but for something running on <1v could cause erratic operation.