One problem related to brake light on has been reported for the 2003 Ford F-350. The most recently reported issues are listed below.
I thought my foot slipped off the brake and taped the rear end of the car in front of me. Scratched the bumper of the car I tapped. I was on I 95s towards fredericksburg, va when my brake warning light came on. Taped brake and the pedal almost went to the floor, but I did have some braking. Got the truck to the repair shop, diagnosed will hole in brake line caused by rust. Replaced 18 ft of line.