Right rear turn signal/brake light out

Are you sure the bulb itself is not bad? Keep in mind, it has a duel element bulb. The driving light may work on that side but the other element may be bad. If the bulb is good, I would suggest checking the wiring where it connects to the trailer wiring.

I had already swapped out a working bulb from the left side with the bulb on the right side. The "burnt" bulb worked in the left side.
There are fuses under the hood for rr turn and brake as well as lr turn and brake. Those were replaced with no effect.

On the trailer socket, I get current when the left signal is on and none on the right signal with each respective signal activated.

Is it likely the short is "upstream" from that? Is the turn signal actuated via the body control module?

I do not believe they were in 2004. Considering the front one does work, it sounds like a wiring issue upstream from the light or trailer wiring. I hate to say it, but it may be time to start tracking wiring to see if you can find a break or damage. I am sure that is not what you want to hear. Before you do that, make sure there is power in the fuse box to the fuse for that circuit. The problem could be right there. If there is not power to the fuse, it will save a lot of time when trying to find the issue.

How do I check the fuse socket? Ground on one lead to the vehicle and one side, then ground on vehicle to the other? and is not there only going to be current when the signal or brake light is active so I turn on the signal or hazards or press the brake pedal?

Hello,

You can check the ground by using a test light. Here is a guide to show you how to do it.

https://www.2carpros.com/articles/no-tail-lights-exterior-running-lights-tail-lights-out

Its for turn signals but you get the idea.

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester

Here is a a wiring diagrams for you

Please let us know what happens.

Cheers, Ken