headlights going crazy on 04 cavalier

My headlights keep going out, but the bulbs are good. Some times my running light works, but headlight will be out. The other day both were out, but couple hours later the right one came on. One time i was driving and my running light icon inside my car was blinking, like to tell me it was out. Then when i got up behind a van i noticed my right headlight was literally blinking off and on the whole time i was driving and my left one was out. Cop wouldv'e loved to see that. Can anyone help?

Welcome to AF, we have a Chevrolet > Cavalier forum that might be able to help you better get the answers you need, perhaps you can find someone who encountered the same problem once and will know what to do. Good luck, and i hope you find everything you need here.