Simple Gas Fireplace using an ESP8266 and a relay

Very interested in this. I have the same fireplace however a little different wiring setup than what is mentioned in the article. My switch wires go to a control box under the fireplace, I assume this is where I would connect the relay?

As you can see in the pics below, the wires on the back of the switch terminate at the control box underneath (pic 2 and 3). You can see the wire coming from the switch through the hole there in the background.

Thanks in advance!