The Iron Barrels two brake light switches are capable of turning on the brake light independently and one (or both) of them must be in the "on" position.
(This assumes you are not mistaking the "always on", tail light for the brake light.)
If it was mine, I would disconnect the green wire from one brake switch and then check things out to see if the brake light was still lit.
If it turns off, you've found the culprit.
If it was still on, I would disconnect the green wire from the other brake light switch.
With the green wire from both switches disconnected, there is no way the brake light can be lit unless there is a short circuit that is connecting the "always on when the lights are turned on", blue tail light power wire to the green brake light wire.
I'm pretty sure the rear brake switch is connected to the brake pedal with a spring.
Make sure that something isn't pulling on the spring or the hook that connects it to the brake pedal arm.