my headlights go out

check fuses sounds like a relay fuse or something could also be a short but most likely a fuse or relay for lights.

I owned 2 chev corsicas both bought here in Newberry sc. A 1988 and a 1989, as of 2007 the 1989 was still running in mi, I had the same problem and it was a relay switch. The Corsica is such a great car but those switches can become expensive to replace. I wish I still had mine. Great Car,Barb