brake lights stay on when ignition switch is on
Try pulling up on the brake pedal. Also try unplugging the brake pedal switch. If lights then go out replace the switch.
Try changing all of the bulbs. Especially the one on the cab. I just went through this with the exact same truck. I took the fuse box relay center out and tested all the wires, nothing. I replaced the brake switch, nothing. I took my dash apart to get behind my display panel, nothing. When I replaced the bulb on my cab the brake lights finally turned off. You can try all of these trouble shooting ideas but deffinately try the simplest first.
It might just be the brake pedal switch. It is a plunger type switch mounted about half way up the pedal itself under the steering column. It can be removed by rotating it counterclockwise about 30 degrees. The plunger has several notches internally so the length can be adjusted in about 1/16th inch increments. It's tough and it feels like you are breaking the switch but try pulling the plunger out. You can play with it until it makes contact with the pedal when installed and releases when the pedal is depressed. I just figured this out on my 2012 Ram 1500
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