You can't change the lighting in one part of the map and not another.
But you can set a trigger so that when the player's units are entering the cave, the entire map's lighting gradually dims; and when they are leaving the cave, the map's lighting gets gradually back to normal brightness.
Crunkatog on ESO
Bart331 balance suggestion: aztec: remove civ
Voltiguer: Ender, Sioux in 1.04 will be a top civ, no matter how many layers of Sioux goggles you put on
schildpad on Elephants: ...their mansabdar unit sucks so hard it looks like a black hole
Crunkatog on Steam.