Why is shone incorrect in this sentence?
The closer I got, the brighter the light shone.
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It's not grammatically incorrect. Its meaning is slightly different from what you most likely intend. How brightly a light shines does not depend on how the light is perceived — rather it's the other way around. So to say
seems to me to imply that somebody was controlling the light, watching you get closer, and increasing the intensity of the light as you did so.
I think what you mean is
This means that the light appeared to shine more brightly; but this was just because you were closer, not because the intensity had increased.