Good news, it kind of failed when I was sitting there. After the thermostat turned it off, I put volt meters on the solenoids and the oil pump junction box wiring and upped the temperature and it did the behavior seen in the first video, then I was able to see something even more interesting in the second video.
I noticed the air pressure gauge was showing pressure but the oil pressure gauge was not. The oil solenoid was however getting 110vAc and so was the oil pump. The unit would of course turn itself off after 5 or 10 seconds as it wasn't seeing a flame via the CAD sensor and this appears to be because there is no oil pressure.
During the second video, you can see me reset the unit a second time around the 20 second mark and then you'll see that there is no oil pressure or flame, then I go over to the pump to show there is voltage to it and right at the 28 second mark you'll hear a click or thump from the oil pump and then you can hear the unit turn on and then hear the normal flame whistle coming from inside of the fire box. To put it another way, the brain energized the pump but the pump did not turn on and there was no oil pressure and towards the very end of the window of time it will continue to attempt to start a flame/fire, the pump made a click/thump, turned on and created oil pressure, allowing the flame to start and the CAD sensor to see the flame and then allow it to continue to run as normal. Also, when the pump is creating 0 pressure, I can feel it vibrating slightly.
So I believe it is the pump that is the cause of it not restarting. I believe the unit itself tries to restart, but gets no oil pressure within the time allotment window that the brain allows for it to start and then goes into a failed limp mode requiring a reset button press to restart. So then the question that comes to mind is, could this be due to some sort of air build up in the pump/lines, or more likely (because of the click/thump clue) is there some sort of solenoid or relay inside the pump that is failing, which starts/turns the motor over therefore creating pressure? Is this common? What's a new pump cost? (do I even want to know)
Cleanburn start up after failure 2:
http://youtu.be/P3lY6T632LECleanburn start up after failure 3:
http://youtu.be/A_VSk3LHiRo