Brake Lights On All The Time

After replacing my brake light switch on my ’65 Valiant because the brake lights would stay on sometimes, now the brake lights stay on all the time. Only by disconnecting the thin third wire on the positive battery terminal do the brake light go out. Also, I noticed that the car will only get electrical power when that thin third wire is hooked up to the positive battery terminal. I thought that wire was just to recharge the battery from the alternator and the car would actually run off the battery (even for a short period) with both main battery cables connected. Other lights seem to work okay, headlight and turn signals. Any help would be appreciated. Seeing red in Kansas!