"John B" wrote in :

Your problem could be simple or complex. Let's hypothesize a simple
case. Suppose the high-tension cable that carries high voltage from
the controller, to the spark gap, is malfunctioning. A major argument
against this is that, according to you and Bubba, your action to reset
the controller by cycling the interlock switch invariably enabled the
heater to successfully operate. Yet if you were wrong on this point,
then the simpler potential faults gain new life.
Consider that your spark cable could be arcing to
ground...intermittently...perhaps based on proximity of the cable to a
sharp metal chassis edge...or even proximity of the cable to the flame
sensor wire. Thus the spark would not occur at the pilot site, the
flame sensor would disallow main burners to be fueled, etc.
You might have an overtemp sensor, or undertemp sensor, that is
putting your controller into a lock-out state.

You DID say that your repairman replace the controller, right? You
ARE presently using a new controller, right?

No. I said:

"A new module was ordered, and a week later another
fellow brought it out to install it, only to find it was the wrong part."

The controller has not been replaced.

Bruce