Max, I have to disagree with you on this.....the ABS module can turn the RED brake light on, but it will also set an ABS code, and the ABS light does not look like it's on(not mentioned)....I would disconnect the fluid level sensor in the reservoir and also disconnect the ebrake switch, one at a time, to see if the light goes out......
Also check to see if there is an ABS code in history and clear it....