My brake lights stay on while truck is running but work normally when truck is off

brake switch bad replace it mine did same thing

if u just replaced radieo or other eqp check what u done

The brake lights work regardless of the ignition switch. There is normally a switch mounted under the dashboard, that presses against the brake pedal hangar. Normally, when you press the brake pedal, this switch loses contact with the hangar, and the brake lights come on. If the switch gets broken or out of adjustment, the brake lights can stay on at all times. This will eventually kill the battery. Readjust or replace the brake light switch.

The brake lights work regardless of the ignition switch. There is normally a switch mounted under the dashboard, that presses against the brake pedal hangar. Normally, when you press the brake pedal, this switch loses contact with the hangar, and the brake lights come on. If the switch gets broken or out of adjustment, the brake lights can stay on at all times. This will eventually kill the battery. Readjust or replace the brake light switch.

It isn't often we get enough information to make a diagnosis, but I think we can in this case.
You have a break light switch under the dashboard that is plastic, and has a "plunger" button.
When you press the brake pedal, that allows the plunger button to extend, which closes contacts inside the switch, and makes the brake lights come on.
If and when that switch either breaks or gets loose, the plunger will stay extended, and the brake lights will stay on, discharging the battery.
God bless your efforts to see & fix this.

most all newer vechicle when turn off ignition.light will turn off automatically.only time use manual headlight switch when malfunction in the automatic lights not turning on manual light design just get you home.

check your brake buster

Try pulling back on the brake pedal if lights go off then either switch adjustment or the brake booster is allowing the pedal to drop down if it's running (vacuum) or brake pedal mechanism is binding.

There is a brake light swich along the brake peddle that need's to be adjusted. Quick and easy fix.

check the rear bulbs