| Ummm. As I read through you post again, I see you are specifying that it's the heating fan relay that clicks. If you can distinguish that from the other relay, you are doing well.
You should hear the HFR click on only when you turn the power on to the furnace, not when the thermostat turns on.
Is that what you are observing?
Try disconnecting a wire from the limit switch --- which should turn on the fan.
Rather than getting voltage to the point that the pilot valve and spark would turn on as I suggested in the previous post, you are losing voltage before reaching that point.
It could be a defect in the three wire pilot, too. You could try tapping that with the handle of a dinner knife or fork to see if that jogs it into operating. When the pilot burner gets old, it wont make the needed connections reliably.
Unfortunately, I can't find a circuit diagram for that furnace off hand. |