Thermostat Where Do The Two Wires From Condenser Go?
Everything at the furnace looks good.







There seems to be an extra cable at the thermostat, which might be an old abandoned two wire thermostat cable.

You'll also notice the C wire just hanging out, which should be either used or capped off.

besides that, everything looks good at the thermostat too.



I'd investigate where that abandoned cable goes. I'd start by looking in/near the furnace. But based on what you've shown, I wouldn't suspect the problem is with the wiring.