Don't even begin to think your problem has anything to do with the
FEM. It doesn't & can't.
If you have the ABS indicator lamp that is in the
instrument cluster on all the time after start up your car most likely has a wheel sensor, there are 4(one at each wheel), that is not functioning correctly.
When the key is turned to the run position the
ABS module carried out a self test by sending out a reference voltage through each wheel sensor to determine if they are functional. If any wheel sensor does not respond the
ABS light will come on & remain on.
Each wheel sensor has a failure code assigned to it. If you do not have a
code reader head on over to a auto supply house like
AutoZone or
NAPA. They will gladly do a diagnostic code read for you. Then you will know. If you do light mechanical work you can change out the sensor. It is an easy task they are plug & play just held in with a clip. Otherwise auto shop or even a tire dealer can do this for you, especially if have already identified which wheel.
Keep us updated on this, good follow up is how we all learn.