Trick question. Am I someone on Earth? (If so, 8 minutes). Or am I in a ship that is hurtling toward the Solar System at 0.999c, roughly in line with the Sun-Earth axis? If so, although I see speed of light as c, the Sun-Earth distance is foreshortened relativistically, so it will be less than 8 minutes between me perceiving the event that the Sun disappeared and perceiving the event that the Earth lost illumination.