Right Rear Lights and License Plate Light Fail after 1 Minute?

I have noticed recently that after about 1 minute on having my lights on, the
right rear tail lights and the right side of the license plate lights are off. They are
on when I start the car, but shut off quickly. I do see moisture inside the rear
light assembly in both the red and white sections if that matters. What would
cause them to stop?