Mfore33, that youtube video does not work.
Have you tried taking your foot or your hand and pull up on the brake pedal to see if the brake lights go out? If that happens, then you should take some lithium grease or WD40 and spray the brake arm up at the top were the pin is located. If that is not the issue, then most likely the brake switch is faulty and needs replacing. It is located straight up the brake arm with I think 2 wires going into the switch. But try the pulling up on the pedal first as it may just be a sticky pedal.
2015 Race Red Performance Package GT 5.0 (435hp) stock
Still in the making Updates coming soon!