I suspect the timer that controls the blower.
Give some more details about the system.

its a gmc furnace located in the basement. its prob 30 years old. if I can provide any info let me know. I am including a pic of it if that helps and thanks!!

Here is a link that might be useful: {{gwi:1596391}}

I'm not familiar with that furnace, but the blower function is somewhat generic. The timer runs the fan for a set period after the thermostat is satisfied.
On a unit that old the device may even pre-date solid state and not be part of a circuit board. That may make isolation and testing easier.
A tech replaced my electronic one for ~$50 parts/labor. Like you say, it was a waste of electricity.

"On a unit that old the device may even pre-date solid state and not be part of a circuit board. "

Older systes used time delay relays that contained the timer.

I guess its not as old as I thought. It has a solid state board and is marked on the decal 1993. its really filthy on the inside. should it be blown out with compressed air? the GMC model number is as best as I can read it GMP100-4 Rev 8 or B. The tech the home warranty sent out replaced a part that made the heater come on but said he couldn't do anything about the fan coming on. he wasn't that great he left the drain tube unhooked, the filter half-way in and cut connections inside the unit instead of throwing them away in the trash can right next to it. I guess Ill call the home warranty people on monday. he did get the heater going though. any thoughts?

I also noticed it has 2 fans a small one above maybe to exhaust CO? It and maybe the big lower one comes on when the door in replace and stays on a few minutes. is this normal? if not it may be a way a tech could check it since he said it had to be on when its not supposed to be before he could fix it.

I took some pics of the inside here is a link to the album.
thanks!!!!

Here is a link that might be useful: furnace pics

My thoughts are that if you aren't going to troubleshoot and do this yourself that you should call an HVAC tech and not a generalized individual. A good tech can test the blower circuit live or dead. The fan should run when the unit fires.
Dirt isn't good for components or connections. If you blow it out how will you know you're not forcing dirt where you don't want it? Use a vacuum with a brush. Be gentle around components. Many synthetic materials become brittle after long term exposure to heat.

On many older furnaces, the fan control is electromechanical, no electronics, and located in the hot air plenum above or adjacent to the heat exchanger. It is not unusual for such setups to shut off the fan after a heating cycle and then for the residual heat in the heat exchanger to cause the fan to cycle on again for several seconds.
Sometimes the burner high limit control is combined with the fan control.

"its really filthy on the inside. should it be blown out with compressed air?"

Using a shop vac (possibly with some smaller extension nozzles) is a lot better than driving the filth further into the equipment.