An ant outside any shadow can see both light sources.
An ant in a non-overlapping shadow cast from one object will have one light source blocked out but the other light source will be visible to the ant.
An ant in overlapping shadows from two objects will have both light sources blocked out. (Geometrically in this case it is necessary the overlapping shadows be cast from two separated points each from distinct light sources)
When one light source is visible to the ant that area must be lighter than when no sources are visible. This is the scenario presented by the OP.
edit: Since people seem to not believe this you can find a representation in part E in this diagram
https://i.imgur.com/r6x6QPQ.jpeg
and a photograph of this nicely done with colored lights here