I may be using the term cycling different than it is used in the
industry.

This is what I hear and see and what i call a cycle. At no point does
the fan turn off and then back on during this cycle.

(a) click click click to light the pilot
(b) then I hear a large gas flame and burning of gas.
(c) then I hear the fan turn on // turns on only once and stays on
until (e)
(d) then i see the gas turn off
(e) then i hear the fan turn off.
(f) then either 1, 5, or 10 min interval later this cycle repeats with
the click click click (step a).

I think Charlie Brown you are a nutball!!!
As you notice in my first post i said i had heating problems with my
last house also.
So yes I am crockydile in the last post. This is no troll of any sort
or to waste anyones time.
If you had indeed read the post you would have noticed i temporarily
replaced the thermostat and changed that anticapator. The original is
back on and untouched.

I am having a problem and looking for suggestions on how to determine
the cause of the problem since
it is becoming expensive.

It appears to me you are trolling to start arguments and take this
thread off course. Please go home charlie brown.