Dim headlight on a 2002 Chevy Cavalier

I have an '02 Chevy Cavalier whose passenger side headlight went dim suddenly one day when I started the car. When I start the car, the daytime running headlights indicator flashes and clicks, and then the service light comes on. I have tried the following:

  1. Swapped lightbulbs between the two lights. It is not the bulb.
  2. Swapped fuses between the two lights. It is not the fuse.

Even stranger, when I remove the fuse to the dim headlight, the light stays on. My guess is that I have a short somewhere in the wiring. I took a brief look at the connection between the socket and the wiring and everything looks good there. Has anyone else experienced this problem? Where should I look for this short, or is the problem somewhere else?

Thank you kindly,
Ray

I would start with the ground connection. And this would be an open, not a short. The problem could also be in the daylight running light module.