The fact that each lever gives different results is potentially helpful.
What happens if you disconnect the lever that shows the fault from the system entirely, and only use the lever that sometimes works?
What happens if you disconnect hte lever that sometimes works, and only use the lever that faults?
Are the brake lights powered directly from the levers? Or from an output on the controller, triggered by something internal on the controller itself? Or do they have their own power supply, and only triggered by the levers / controller?
If the first or third, and are LED rather than incandescent, then they could work even if the switch wasn't working quite right, as the current to drive them would be low--they also wouldn't be susceptible to switch bounce or other intermittent-contact issues; you'd see a steady light even with that in most cases--but the controller could detect such a problem and could be designed to show a fault and not accept such a noisy signal.
If the second, then the controller is actually accepting the signal, and correctly triggering the brake light, but has some software portion that processes the brake / regen signal differently before sending to the motor control, and that part could be corrupted or buggy, or just doing the same as the first and rejecting the signal even though it does accept it for the brake light.