It does sound like it could be the switch on the break pedal. That should be easy to swap out. Before you order it, just crawl under the steering wheel and take a look at the brake pedal switch. It should be easy to spot. Make sure it is not stuck oen/closed. Also make sure there in no interference between the switch and the peddal asembly and lastly make sure the peddal asembly is complete in order to activate/deactivate the switch.
Good Luck!