Time not stopping for light, but (almost) everything else, would cause a whole lot of problems. Sounds like a nice scenario for What If
If we take this in consideration and assume, that his equivalent of air is also affected and therefore cannot be moved. The affected would be stuck and unable to move and die of asphyxiation in a dark void.
EDIT: Another interesting factor to consider is, that if the affected were able to move, he would have an undefined acceleration due to delta v / 0.
I saw a short story about a hero who could stop time but he could only see things he was looking at before he stopped time or was walking towards so only looking directly ahead. It was established by a thought experiment or something that addresses the reader. I really wish I could remember the name of the story but it was so long ago I don’t think I could remember the name even if I heard it