I'm relatively sure that the issue is stray light or light leakage. I've seen a similar image posted here on Nikonians. Like your images, the problem was confined to situations where bright sun was hitting the camera body - and probably the viewfinder.
There is a smaller possibility that you have light leakage through the lens. The AF distance indicator leaks light on some lenses, but that does not look like the issue here.
The choices to deal with the issue involve shielding your viewfinder from direct sun. That can be done with a small lever on the D800 but not the D600. Your best choice is probably to shade the viewfinder with your hand, a hat, or something similar. I typically simply hold my hand just above the viewfinder.
Even if you don't have major light leakage as in your images, it's easy to change the exposure by a stop or two due to light leaking through the viewfinder. Holding your hand or something over the viewfinder is a good practice for all images where bright light hits the camera.