No taillights, break lights, turn singnals, nothing

Hello, I'm Danny.

Yes, the brown wire if broken controls all the rear exterior lighting. Here is a tutorial showing how to test wiring:

https://www.2carpros.com/articles/how-to-check-wiring

I've attached an exterior lighting wiring diagram below for your truck. I've circled in red the areas where the brown wire is routed. I enlarged a few pictures so you can view larger. You should just be able to repair the connector or splice the wire to fix. Just be sure to use heat shrink tubing after repair to keep out moisture. Hope this helps and thanks for using 2CarPros.