My furnace doesn't seem to start when the thermostat calls for it to
start. Sometimes it does, sometimes it doesn't. When I place a meter
across the thermostat terminals (T to T) on the controller (Honeywell
R8184G1286) the Beckett AF burner starts and runs for several
cycles...perhaps a week's worth but then won't start until I touch my
meter probes to the T-T terminals the next time.

Any thoughts would be appreciated.

Boden