I have an old overhead Air handler (mounted in the bathroom above ceiling) and the blower FAN switch is set to AUTO Heat but the fan never turns on...Thermostat has been check but the A/C repairman ca

Could be a bad blower motor resistor,mounted by the blower.

open it up and vacuum and blow out the fan and other areas

the fan fill come on with the sequencer (stack switch you call it) it will also come on with the fan relay. on some goodmans the fan relay is the black box on the circuit board. use a jumper to jump red to green, this should bring the fan on sounds like you could have a broken green wire, try using a different wire instead of green

Sounds like a sticking relay. You can check the stat simply by remove the faceplate. If fan still runs with tstat cover off its not the stat. Not sure is your blower has a separate relay or if relay is mounted on control board. This can be bypassed with a new relay if you are willing. Good luck!!

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It the wall themostat set to AUTO or MANUAL on the FAN switch?
It should be on AUTO.
I saw you chat question. Intersting that the board is new and the fan would misbehave. It must be something simple like I suggested above.

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Check the fan relay switch in the air handler.
Check the fan motor capacitor.
Check the fan blower wheel for binding.

If you have a standard thermostat the fan switch is for the air handler only. It completely over rides the thermostat for most settings. Now lets see this is what I'd expect:
fan switch on Indoor fan runs all time
Fan switch auto Indoor fan only runs when thermostat is set to cool or heat and the thermostat is turned up above room temp for heat or below room temp for cooling. In both of these modes the furnace blower comes on and stays on til the room temperature is satisfied. The outdoor unit only comes on for AC the out door unit will not come on for heat or the "on" setting on the thermostat. See exception 1 & 2 below...

Exception 1- (in a heat pump the out door unit runs in both heat and cool mode unless it has emergency heat turned on then it will not come on outside in the heat mode, and depending on the type of heat pump and furnace or air handler it is). A heat pump thermostat usually has "backup heat" and an "emergency heat" setting switch on the thermostat.
Exception 2 - On some thermostats they are made to cycle on the heat if the temperature reaches a preset temp (around 50'f usually but definitely by 40'f). This mode prevents freezing when if instance the homeowner is away or while the home is under construction. In this mode the fan inside can run but the heat usually comes on with it.
Exception3 - On some electric furnaces the heating strips may be individually controlled and thus not all come on at one time. This may give the feel of no heat especially if the room is cold.

Now there may be other exceptions but Ive tried to give you a heads up on some of the most common ones.
If you need more help please post more specifics about your unit/system as to for sure what switches are set to what setting and what is happening with each. My first though was that maybe your system is OK and you needed to know if the thermostat was working properly.

If this helpd you understand your problem would you please give me as hifgh a mark as you can. Thnaks for using fixya and good luck.

The fans are set to delay for 60-90 seconds to remove all heat from the heat exchanger/heater elements.

If the fan runs any longer than 3-4 minutes after the Emergency Heat shuts off, you may have a bad sequencing relay in the air handler.

is this a new problem? the fan speeds can be adjusted by changing wiring connections. If it is a new problem on an existing system then it could be the t-stat or a problem with the curcuit control board. the switch on the t-stat for FAN is set to auto not ON. if set to on the switch to auto - problem solved.

the fan is controlled by a fan center or a stack switch. as burners light and heat up the spring sensor on the bulkhead above burners heats up and turns and a a point energizes the indoor fan if it gets to hot the burners go out on safty. sounds like a fan control is bad tap on them gently and they sometimes break loose but if not then have a pro replace fan control and test heat exchanger.