What type of Thermostat. Many T-Stats today are digital electronic and have an internal battery. if dead no joy
My RV from factory used one of the A/C's to control the furnace (Front one) when I replaced the A/C I had to put in an new furenace stat
I got a 20 dollar mechnical mercury free (This is improtant) from Ace Hardware and a toggle switch and an LED indicator
Of the two, normally blue, wires one has 12 volt on it. this goes to the toggle (Which is mnounted beside the T-Stat I choose a rocker type) the other lead of the switch goes to the POSITIVE lead on the Led an the T-Stat
The other T-Stat lead to the other blue wire
The negative LED to Ground (it is a 12 volt LED indicator assembly)
Switch off = Furnace off
Switch on = LED on T-stat controls furnace
LED blinking (Slowly)( or dim = problem with wiring back at furnace