Here is a TSB that came out quite a while ago that fixed my problem very similar to what you describe. Seems to be almost exclusive to the 2000 yr model. Replacing the insulator tips on the mounting bracket travel stop tabs works like a champ. The TSB has a diagram illustrating the fix.

http://corvetteactioncenter.com/kb/q....php?qstId=217

2000: Service Bulletin: Left Headlamp Door Does Not Stay Closed
Number: 00-08-42-002
Subject: Left Headlamp Door Does Not Stay Closed (Shim Headlamp Door Motor/Actuator and Replace Insulators)
Model Year: 2000 Chevrolet Corvette

Condition: Some customers may comment that the left front headlamp door does not remain closed after the headlamps are turned off. Others may comment that the left headlamp door closes when the headlamps are turned off, but then reopens. In either case, the right headlamp door operates properly.

Correction: Important: he following information applies to the left front headlamp door motor/actuator only. It does not apply to and should not be performed on the right front headlamp door motor/actuator.

Install one washer (2) between the left headlamp door motor/actuator (1) and the mounting bracket (3) at each of the three attaching bolt locations. Also replace the insulator (4) on each of the two mounting bracket travel stop tabs (5) as shown. For information on headlamp motor/actuator removal, see the Headlamp Motor/Actuator Replacement procedure in the Lighting sub-section of Body & Accessories in the appropriate Service Manual.

Parts Information

Part Number
Description
Qty Per Vehicle

11505463
Washer
3

16524060
Insulator
2

ORIGINAL: kruser

My battery went dead on my '98 vette. Today I came home and both my headlights were up. They came up by themselves, so I jump started my car, put the lights down, killed the engine and was walking away, and one headlight just came up. Anyone see anything like this before? I have noticed something drawing my battery dead if I don't drive it for a couple of days. Anyone have any ideas? Maybe a relay? Thanks for any advice.

Kruser

ORIGINAL: 91silverc4

My problem with a 1997 C5 coupe is that the headlights will not come on and also will not pop up when the lights are turned on. All other lights work okay. The only time the headlights will work is if you hold the bright light switchlever continuosly. The regular lights do not come on, only the brights when the lever is held. If anyone has experienced this problem or knows the reason why this happened it will be greatly appreciated.

Thank you