I have a 2011 so my situation is a bit different, but..

At night, the backup camera has a very distinct "black and white" effect.
ANY bright light can be nearly blinding.

I say this because it makes me wonder if it's really your license plate light or another light source. Street lights nearly drown everything out at night (from the backup camera's point of view).

I'll try to take a picture next time (as I do have a street light in my rear view backing out of the driveway at night).