Success! While I am not qualified to give a definitive cause(s) and solution(s) on something so complicated, it is my belief that many of you were correct about the issue(s) and that without all of the different POV's this would not be resolved. Thank you everyone. Read on.
Summary:
- The rain likely had nothing to do with it
- The cold + the first 50 miles in 18 years caused a self-adjustment (gunk, particles, etc.) of the choke/idle
- The ceramic resistor was causing a weak spark
- The clog/self-adjustment of the carb made the mix leaner and the weak spark was no longer able to ignite it as before.
- This would explain why the PO, who had the car methodically serviced the car prior to 2005, would have never noticed the superfluous resistor as long as he kept on top of the carb tuning, etc.
Short Term Resolution:
- Remove ceramic resistor from (+)coil circuit
- Adjust choke/cold idle
Long Term resolution:
Permanently remove ceramic resistor from circuit
Rebuild carb (thanks @John76 )
Process (hours of overly cautious prodding condensed into a one minute read):
- The fuel pump was working extremely well (thanks for the step-by-step test plan @Mike Self)
- After bypassing the ceramic resistor we saw signs of life (spark) but it just couldn't quite get going (thanks for the incredible catch and test plan @'76mintgrün'02 @Dudeland)
- Adjusted the choke (having never spent a minute with a carb thank you Youtube)
- It's started right up. However, whereas on the warm day that I picked it up from the mechanic and the cold idle was too good to be true for a car that sat for 18 years, it now required that I give it a little gas to keep the engine running.
- after a few minutes of babysitting the idle it warms up and runs just like the day I picked her up (moves off of cold idle cam step)
- Adjusted the idle screw (again a complete rookie's touch) and things are looking like a 'win' for Team 2002FAQ.
As with any such 'project' I came away with more questions/issues about this car than I went in with (now the horn honks when I start it), so there will be many more posts to come. Thanks again everyone!