Furnace Inducer Whirrs on and off before igniting, works when I tap circuit board
Tracking down an intermittent problem like this requires being careful and methodical. 

First, take Ed Beal's suggestion pull the switch out so the furnace runs without the cover. Then, start tracking results. Are you sure that tapping the circuit board fixes it? How about wiggling the wires, one by one? Or, can you cause the problem to occur (not go away) by wiggling something?

Eventually you'll narrow it down to the flaky component, but it may take a while. Good luck.