At the furnace, if you connect the R and G terminals with a wire the fan will run. I used a Shelly 1 for this because the relay is separate from the voltage used to power the Shelly.
The Shelly 1 is connected to 120v power, and one wire for the relay is connected to the R terminal and the other wire is connected to the G terminal. On my furnace these wires carry 24v ac power and turning on the Shelly closes the circuit and the fan runs.
I created a thermostat card that has 3 fan settings. Auto, On and Circulate. The On button calls a script that turns on the Shelly. The Auto button calls a script that turns off the Shelly and the fan is controlled by the thermostat. The Circulate cycles the fan on and off (10 min on, 20 min off).
