Check your Brake Pedal Position switch. The brake lights should not go on unless the pedal is depressed and that switch is active. Sometimes the switch can get knocked around and not connect with pedal lever, but that usually results in no brake lights going on. The only other way for a brake light to go on is if there is a short in the wiring. A shorted brake light is not going to affect transmission shifting, but other electrical issues in the wiring harness might. You're 4L60E is electronically controlled, so you may want to inspect the harness and look for abrasions, exposed wires, chewed wires, etc., that might affect it.