Brake issues

Does this very same brake warning light also come on if the parking brake is on? If so, you may want to check that it is not just the parking brake, so find and disconnect the wire at the parking brake switch and see if the light remains off.
It should be a single dark green/white wire at that parking brake switch.
That switch should be located on the parking brake mechanism.

Well, the brake system is not supposed to turn on that light until at least the brake pedal is pressed down and senses a pressure differential so if the light is just coming on without even pressing down the brake pedal and it is not the parking brake switch wire, then it has to be a shorted brake warning switch or a short in the wiring. Let me get the wiring diagram and see exactly what is involved with that warning light, hold on one second.
Actually the repair manual says a faulty brake level switch can cause that, so have you also disconnected it as well?

I am not really sure if and when the brake fluid is empty or full if it opens or closes that brake fluid level switch, so if you disconnected the switch and the light is still on, try grounding that dark green/orange wire at the level switch and see if the light goes out now.
I would also leave the parking brake switch disconnected as well until this is fixed just incase you have a problem with both.
Other than that since that level switch feeds directly into the front control module in the integrated power module, perhaps retrieving the trouble codes from it if possible, the BCM and PCM as well might shed some light on the situation.