I have been trying to diagnose this for about a month now and now I’m reaching out for help. To give an overall synopsis.
1. I have removed the brake switch and replaced. I have manually tried to press the button and the lights remains on.
2. I unplugged the combination blinker switch and the lights go out but third light remains on. I replaced the combo switch and still have the same problem.

The only way to turn them off is to pull the main fuse under the hood which is done just to save batteries.

Any help is greatly appreciated.

 

Does your truck have cruise and does it work?

IMO you can have a brake switch that stays on (or you try to lift the brake pedal and see if the light goes out- pedal return spring) or a short in the wiring that makes the brake light stay on.

 

It has a cruise but unsure if it works due to drivetrain in shop.

 

If you unplug the brake switch (without removing it from it's bracket) does the light stay on?

 

Yes it stays on.

 

OK, it is a wiring problem then.

You say it lights up as soon as you connect the battery? (And have the fuses installed)

It seems that you get a permanent hot to the brake light hot somewhere-
I'd try to start pulling the fuses in the cab one by one and note if/when it goes out.
This could help to identify the source circuit.

Did you do anything to the truck before this started or did it just come up with it out of the blue?

 

Another possible solution: