Upgrading older White-Rodgers 1F80-51 thermostat to a Honeywell WiFi RTH9585WF & attaching a C wire

I upgrade an older White-Rodgers 1F80-51 thermostat to a Honeywell WiFi RTH9585WF. This includes hooking up and attaching a C wire that was present but not connected in the furnace, at a splice, or at the old thermostat. There was some funny-business by the prior thermostat installer: the brown wire was connected to the RC terminal in the thermostat despite not being connected elsewhere, the RC-RH jumper was extremely loose which may have led to intermittent cooling, and I discovered later that the thermostat was set to "Electric" rather than "Gas".