Recently my passenger side taillight went out, I replaced the bulb but it still wouldn't work. I checked and the light comes on when using the turn signal and when the brakes are applied. My next best guess is a problem with the wiring harness? Anybody have any experience with this? Or other suggestions on where to look for a problem?

Just to clear up the light works when using brakes or turn signal and does not work when lights are on. I've seen other posts that have the issues reversed.

 

Using a 12v tester, do you have voltage to the "running" light socket?

 

Maybe you found the problem already. I had the same problem. Look at the trailer wiring harness where it passes between the chassis and the body at the rear door You will have to open the door to see it. It should be right above the license plate. that harness was pinched and worn thru to ware it was shorting out not only the right turn signal but also the license plate light . There is I believe is a 13 pin connector that I ended up having to replace with a 8 pin connector. Not hard to hard do just took some time or maybe just need to splice some wires together.