I think these cars have lamp circuit sensing. It may be caused by a blown lamp or incorrect lamp (wattage). This is only a guess, but I have seen it in other makes/models. Good Luck The DRL relay inside the gauge cluster has been blown. The only way to fix it is to either replace the whole cluster (easiest) or dissemble and replace the DRL relay.
Turn on the headlights and walk to front of car and see if both headlights are on. Make sure to check both the high beam and low beam head lights. I believe that the blinking light you are seeing is to tell you that one of the headlight bulbs is burnt out and needing replacement. That's the Daytime running light indicator. Check that they are working.
This is caused by one of your headlights being out most likely the brights. turn the car on switch from brights to normal and daylight lights and you will see on is out, you just need to replace the headlights Did you find out the answer? I want to know because mine is doing the same thing. Thanks! firstname.lastname@example.org Along with the blinking you should hear clicking, the clicking is a faulty daylight running light relay. The DRL Relay is the located in the fuse box. I installed HIDs in my 04 cavy and when the daytime runners are used they do not supply enough power to the Catalyst. so i have to turn them on manually to get them to stop blinking. (daytime dash light also blinks) its kinda cool when u accidentally pull someone over with flickering headlights lol. i just wanted to throw my personal experience curve ball.
If you're talking about the green head light indicator to the upper left of your speedometer on your dash, that's the daytime running light indicator (DRL). The high beam indicator is a blue indicator and is inside the speedometer arc. A lot of people confuse these two indicators. The daytime running lights may be disabled by preferably removing the DRL fuse in the fuse box in the driver's door jamb or engaging the parking break.
the answer is one obvious fault; from one of two probable problems: the buggered part is the DRL module [Daytime Running Light], but it may have just been the module's time to go, or it may be a manufactured defect in the cavalier's wiring loom, located just inder the battery tray at the left front corner, causing a short circut, thus cooking your DRL, killing your headlights, and causing the flashy 'we've got a problem' light to show on your dash