This is usually cause by a stuck brake light switch on the brake pedal. Replace it.
There is a switch under brake pedal. This switch controls the brake lights. They some times go bad. Have someone stand behind vehicle while you push on brake pedal, if no brake lights come on. Try pushing the brake switch by hand. Check for power with a voltmeter.
Check the fuse, bulbs or there is a push button switch above the brake pedal that may need align or replace
Engaging your parking brake should turn off the daytime running lights
faulty brake switch
The brake light switch has failed
If the brake lights stay on that probably means the switch on the brake pedal that activates them is defective.
Typically your dash lights go out when you are driving with no tail/brake lights. So check those fusses to see if one is blown, this is a safety feature.
The most common cause for brake lights to be out on a 2001 Mustang GT is a blown bulb. There are some instances where there is faulty wiring.
Check bulbs - they are double filamented with the smaller being for stop lights Check for a blown fuse Check the operation of the stop light switch
They are burned out.
open fuse box, pull fuses until you find the one that is burned out. then replace that fuse. VOILA! brake lights work again. I think all dodges have a diagram of the fuses in the fuse box cover just find the brake fuse and replace it.