I know little to nothing about HVAC but, have researched enough to start thinking the following (uh-oh, now I'm thinking again):
There is a sensor function that tells the fan that the air is warmed and it should turn on to blow that warm (and continuing to be warmed) air through the system. When a cycle first starts I can hear the burner come on and shortly thereafter the fan kicks on. There may or may not be a sensor function to tell the fan to continue running for a bit after the burner shuts down (I have not tested this to a conclusive result yet) to flush the ducts of warm air(?).
I am guessing (still really, really guessing) that this sensor may be shutting off the fan as per normal at the end of a cycle. Then something (fan limit control?), correctly or incorrectly, decides that the air in the exchanger (new term for me) area is still too warm and kicks it back on, passes the decision to the part of the circuitry that decided the fan should be off and so turns it gets turned back off and so on, for a couple of times.