2001 Chevy 3500 tail light problem

Hi all. Problem with the tail lights is there isn't any. I have brake, backup and turn signals but no tail lights. Checked the obvious things bulbs, fuses. I really dont know alot about cars. Any help would be appreciated. Also, when I hook up my trailer,that has all the running lights and rear lights. Not sure if that helps.
Could it be corosion? Broken wire? Dont want to spend alot of money to solve the problem. This is a work truck so is there anyway to bypass something to wire on another set of lights so I have tail lights?

Thanks in advance.