Bright lights won't work on my 1999 Cavalier. I've replaced lamps running light relay and checked the wiring harness. When I go from low beam to high beam the low beams go off and only the running lights come on I also get no blue bright light indicator on the dash. How exactly do the bright lights work?

I too had the same exact problem on my 1999 Cavalier. I replaced the lamps,then the DLR,and then looked at the harness under the battery box.(It appeared to look ok and didn't have any corrosion on it I could see). I then ordered a new turn signal/high beam switch that's on the steering column. I replaced the switch and still had the same problem. Not wanting to let this defeat me I started tracing the wires from the high beam lamps back. When I got back to the wiring harness under the battery box I noticed that just one of the wires had a little corossion on it. Guess what? it turned out that was the high beam wire and it was coroded through and not making the cicuit complete. I cut the wire at the coroded spot, restripped both ends and twisted them together. At that point I tried all the lights and they worked perfectly. I then soldered and shrink wraped the repaired wire. (Finally end of problem) My suggestion,Really look closely at that wiring harness. If you have to use a magnifiying glass do so.
This was a really frustrating problem that I finally solved and I hope this can help others with the same problem. I too had the same exact problem on my 1999 Cavalier. I replaced the lamps,then the DLR,and then looked at the harness under the battery box.(It appeared to look ok and didn't have any corrosion on it I could see). I then ordered a new turn signal/high beam switch that's on the steering column. I replaced the switch and still had the same problem. Not wanting to let this defeat me I started tracing the wires from the high beam lamps back. When I got back to the wiring harness under the battery box I noticed that just one of the wires had a little corossion on it. Guess what? it turned out that was the high beam wire and it was coroded through and not making the cicuit complete. I cut the wire at the coroded spot, restripped both ends and twisted them together. At that point I tried all the lights and they worked perfectly. I then soldered and shrink wraped the repaired wire. (Finally end of problem) My suggestion,Really look closely at that wiring harness. If you have to use a magnifiying glass do so. This was a really frustrating problem that I finally solved and I hope this can help others with the same problem.