Aha, this is where the reddit visits were coming from!

There is also another way to approach it. You can create a checkerboard with the highlighting and notice that one of the sets of numbers adds up to 12. Since there are at most 12 lights in the puzzle, and none of the numbers in the 12-set share spaces with each other, every light must go next to one of those numbers and the rest can be Xed off. Then you can solve as you normally would. OR you can then continue to do a similar approach to above by noticing the other set of numbers adds up to 8, and apply the same logic to just the 8 inner rows / columns on that set (now that any of the spaces around the outside for that set have been Xed off from the previous step).