It is kind of hard to explain in detail but if all your lights are working but as your friend said they are dim or if activating the right turn for example also activates another light, you have a missing ground some place.
If you are correct about the green and yellow, the black will be the tail light wire and as Doug said the three whites are going to be chassis grounds. The heavier white is most likely the ground from the chassis and the lighter gauge whites are most likely from other lights.
This is where a VOM or a DMM is invaluable. A VOM is an analog VOLT/OHM meter and a DMM is a digital multi meter. A test light can be used in lieu of a meter in many cases.
Using the OHM scale on the meter, touch one lead to a know chassis ground and the other to each of the white wires in turn, one will read zero and the other two should show a raised resistance to ground. The two with raised resistance feed lights somewhere else in the RV. The one without resistance is the chassis ground. Assuming you have standard dual filament light bulbs in the fixture, turn the tail lights on and touch the chassis ground to the common from the new fixture and the black from the RV to one of the colored wires from the fixture and then the other, The brightest light is the brake/turn light and the dimmest is the parking light.
Doug is usually right and so connect the three white wires on each side to the common from the fixture. Connect the black from the RV to the tail light wire and the yellow and green to their respective brake light wires.
Check what you have done and make sure all the brake/turn lamps, tail lights and DOT lights are operating. They should be. The license plate light should also be illuminated.
Then report back on your test so we know we helped.