Air handler will turn on and off every 10 - 15 seconds then start to smell like smoke

Is it happening during summer cooling OR during winter heating.if it is happening during heating, the question is understandable.But if it is during cooling, it looks strange. If it is during heating your blower may be connected to heater and once the temperature is reached it should stop heater first and then the blower.Perhaps in your case, heater is not being actuated while the blower stops and hence the insulation burning smell.

It is with the heater on a 14 year old system. I can see the heating coils light up and in a few seconds the fan comes on and cools the heater coils then the fan goes off and it repeats this cycle. The outdoor unit does not come on during this process. Used to be able to reset the unit by cutting power and resetting the unit. It would run fine until it was real cold outside. Now when I reset it does not reset. This is a york 10 seer heat pump. I thought about changing out control board but it is really expensive