Brake lights constantly stay on, even when car is not running on 1993 Honda Civic

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I just bought this civic, the brake lights are constatly on. Only way to turn them off is pulling fuse under hood. I realize the switch at the pedal needs adjusting, I replaced the switch anyway, and still have the problem. I noticed the nipple on the brake switch itsekf is not contacting my pedal. And I believe there is suppose to be some kind of bushing or grommet that is suppose to be on the pedal piece and there is not. What advice can i get. I either uave constant brake lights or no brake light cuzI have pulled the fuse or my battery goes dead
(1) Answer
Yes , there should be a little rubber pad on the brake pedal arm. free play on the pedal (check by pushing with hand) is 1-5mm.,pedal height should be 6.5 inches (Measure without floormat). Pedal height is adjustable at pushrod hooked to pedal , if necessary , loosen locknut and turn with pliers as needed.