Re: trailer lights
What I say below will seem elementary, but it will help you troubleshoot if you understand exactly how the trailer lights are setup:
Typically, there are 3 types of lights: 1) tail light 2) brake light and 3) turn signal light (left and right).
Each light needs 2 wires (positive and negative (ground)) to work. Usually, the ground wire is the trailer--the white (ground) wire is tied to the front of the trailer and then each light kit ties it's ground to the bolt that you use to mount it to the trailer, thus, using the trailer as the ground wire extension. You can just run a 2 physical white wires from the front of the trailer to both sides (left and right) if you want. So...in the front of the trailer, the two white wires would be attached to the single white wire on the wiring harness in the front. However, you still need to attach this white (gnd) wire to each light kit. Some light kits provide you with a white wire sticking out the back, but some internally connect this white wire to the bolt (so it's difficult for you to access it). You need to check your light kits and see what type you have in order to determine if you want to run a ground wire or use the trailer as the ground wire.
The next handy thing to know is that the turn signal is the same as the break signal except your vehicle's electronics make it turn on and off. So, the turn signal is just turning the break signal on and off repeatedly. That is why you only need a two wires (brown wire for tail light) and either a yellow or green wire (for brake and turn signal). I am not counting the (gnd wire) because you need that for all lights.
Also, do not connect the white wire to any other colored wires such as green, yellow or brown. This will short out the circuit.
One more thing, I suggest switching to LED lights because you will not have to replace bulbs and worry about them busting or burning out. But...they cost a lot more.
Hope this helps and sorry if it is too elementary.
Can you guys explain how to run a separate ground wire for trailer lights ? Does this mean you connect a ground wire to the green, yellow, and brown wires then ground them with the white wire on the trailer plug or what ? I'm having a ground problem too. The vehicle ground is good and all the lights on it work like they should. . I have the trailer hooked to the vehicle while testing the lights. On the trailer I'm getting a dim right turn signal and no running lights.

Brakes and left turn work good. The ground wire on the trailer is clean and tight. All the bulbs are the right ones as far as I know. This is a Genesis galvanized trailer.