Look at the bottom of the master cylinder.
There is a two wire connector. Disconnect that. See if the light goes out.
The MC has a float with a magnet. When the float bottoms out (low fluid) its magnet makes the proximity switch (the one I said to disconnect) close its contacts.
There is also a switch on the parking brake. It has one wire. Disconnect it. See if the light goes out. It is a ground-seeking wire, turning on the brake light if the pedal is depressed.
You also have an ABS valve on the frame rail. They have a bad reputation for failure too. I don't know if it could cause your symptom.
If your pedal is firm, I see no need to bleed the fronts in your case since you didn't open that separate fluid circuit.