Might be a good idea to give us the MODEL of the furnace.
Sounds to me like the sail switch. On some of the Atwoods they have couple of crappy wire taps off of the control board. I know one of the blue wires that feed the sail switch feeds off of one of the two taps. While the furnace is running I shook/moved the wires in front of the plastic cover over the heat exchanger blower and the blower would stop.
That switch your referring to, I believe its a circuit breaker.
I'm sure others will chime in.
Thanks for the post.