I'm surprised no one mentioned this, but something you could try is to keep a history of where the player has visited, and fully redraw the light over a regular screen sized texture. You could use a deque, and erase 'old' data.

Instead of storing the result, you store the process which leads to the result.

My 2c.

That would be ALOT of locations to store (player can move per pixel, so that would quickly become thousands of locations to store and then all these would be drawn to a screen sized texture each update?).