03 Trailblazer Highbeam relay squeals lights come on by themselves

Hi,
Last week my wife's battery in her 03 Trailblazer was dead in the morning. I jumped it and it seemed fine all day. That night I tried to start it and it was dead again so I replaced the battery. The next day, she looked out at the parking lot at work and her lights were on after it sat for a while. She could not turn off the headlights no matter what. She said she heard a squealing noise under the hood. I could not duplicate it when I got home, so I replaced what I think was the lowbeam relay. Later that night I looked, and her headlights were on. I got under the hood and the highbeam relay was squealing. I removed it and the lights went out. I replaced the relay with a new one, but the relay immediately squealed and the lights went on. I have the relay out now and the problem is gone, but we have no highbeams.

Can anyone help me diagnose what is causing the relay to squeal and turn on the highbeams, or is the darn thing haunted??:biggrin:

What is the battery voltage now?