Based on your description of how you get the brake lights to go off, I would say the simple answer here is the brake switch is failing or worn, or the brake pedal is not returning to its rest position.
Check operation of the brake pedal first to see if there is anything you can do to improve its function. There may be something causing it to bind and not return fully. If that all seems to be working fine, I would lean towards the brake light switch being faulty.