If you are seeing that dimming of the lights and dropping of the volt meter, it is likely just the grid heater cycling during warm up. That is perfectly normal.
What I was referring to was brief moments when the interior lights or dash lights would go out intermittently or randomly in conjunction with your power outlets. As crazy as this sounds, broken wires in the B pillar leading to the back door rubbing together can short those circuits together and cause a intermittent failure. I had that exact issue with my '07.
These trucks are plagued with weird electrical problems that are often unrelated to the symptoms you are actually having. Many times it is the TIPM or PDC (depending on your truck year) itself causing these random issues. Don't jump in to changing it out yet since there are so many other possibilities for problem sources. However, keep it in the back of your mind if you start seeing multiple unexplained failures.
Keep us updated with other symptoms and hopefully we can help you track this down.