I have a dual energy electric/oil furnace that is wired to a thermostat with 2 wires R and W. I don't have any AC. Inside the furnace there is a switch relay to control the fan but it is not connected to the G terminal inside the furnace. I would like to run a 5 wire cable from my thermostat and the furnace and connect the W R and G wires to use the Auto / On fan switch on the thermostat instead of the switch relay inside the furnace, and eventually the C wire as well.

Since the G terminal inside the furnace is not connected to anything, how can I connect it to achieve what I want?
Should I bypass the manual switch or an I wire the thermostat in parallel ?
