Here are your parts includes a wiring diagram
Replacement parts for FRIGIDAIRE FRS22ZGEW2 | AppliancePartsPros.com
The evaporator fan usually stays on except when you are in defrost mode.
Usually half an hour or so every 8 hours.
Sounds like you have a defrost problem. The unit will run OK for a few days till the evaporator coils again get clogged up with ice/frost again.
This can be caused by a bad defrost timer, defrost thermostat or defrost heater.
The defrost timer looks like it is under the freezer side of the unit.
See Item 23 A in the "Controls) section (at bottom of the list)
Turn the cam till the fans & compressor shut off.
Note it only turns in one direction
You are now in defrost mode.
With the evaporator coil cover removed see if the element heats up.
Be careful do not burn your fingers.
If it does odds are high that the timer is shot.
Another test of the tiner is to mark the where the cam slot is, then leave it for an hour or so. If the cam has not moved the timer is not advancing so it is probably shot.
If it does not it could be the heater or the thermostat but this test does not totally rule out the timer as it's contacts may be shot.
Easiest way is to check the thermostat (0 ohms when frozen) and heater (usually around 20 ohms) for continuity using a meter.
Note the thermostat must be frozen as it open a few degrees above freezing.
Here is a good site with fridge repair help
Refrigerator Repair Guide: How To Fix a Refrigerator - ACME HOW TO.com