I had the same trouble with mine. If you remove the brake lever to expose the switch face, you will be able to work the switch out by gently prying on the sides with a small straight bit screwdriver, while pushing the cable firmly into the brake lever assembly.
The switch is hot glued into place and should pop loose with a little persuasion. The cable is not molded into place, it simply passes through a small strain relief into the switch body.
Upon removal, you will see the well into which the switch is placed. If the switch is pushed too far down into the well, as was the case with mine, the brake lever will not make contact to open the circuit for proper operation. To fix the problem, clean out any adhesive residue in the well and glue the switch back in at a higher position. To determine the correct height, I made some cardboard shims to gradually stack the switch up, testing it at each new shimmed position.
Andy