I am no genuis, however, one may want to look at the wheel speed sensors and the wiring thereof. Why? because I BELIEVE that each sensors constantly computes each wheel speed and if one slips or looses traction could activate the ETS so if there is a faulty sensor or short on a wire the computer couls be getting false readings. Another slight POSSIBILITY might be to get sensor spray to clean them becuase you say that the ETS light activates when you brake and perhaps brake dust interferring with an already dirty sensor or when you brake the suspension dips and rubs on an exposed wire which has lost its insulation from rubbing over time.

You may want to do as search on this forum section not just ETS but also on abs etc