Furnace shuts off normally but then fan comes on a few times
I have a 25 year old Day & Night\BDP gas furnace (model 394GAW) with a BDP air handler (model 518A). My thermostat is a 2009 era Honeywell FocusPro TH6000 series. We fired up the furnace for the first time this winter and noticed some odd behavior. It heats the house just fine but sometimes when the interior reaches the desired temp and the thermostat shuts off the furnace and eventually the fan, the fan will come back on for about two seconds, shut off, come back on for another two seconds, shut off, and then pop back on for, you guessed it, another two seconds before turning off permanently. Sometimes the fan will come on only once after the first shutdown. None of the settings on the thermostat have changed since last winter.
It's an annoyance more than anything (the extra times the fan comes on wakes us in the middle of the night) but I do wonder if it's a symptom of something more important here. I've searched the web and all I can find are references to the fan not shutting off until it's blowing cold air (not a problem for us) or the fan not coming on at all (ditto).
Thanks for any advice you might have,
Nick in Palm Springs