The headlight doors on my 1998 vette will not open

located on drivers side of dash board open door and will see access panel number 33 and is a 15 amp fuse following link is owners manual page 138 starts and shows all information for fuses
1998 Ford Explorer Owner Guide 1st Printing

The problem lies in the door frame then. You will need to remove the push button in the door frame and check if it is grounded. You should have noticed that your dome light also stopped working. This is because it doesn't know when the driver door has been opened. Therefore, no alert that you left your headlights on, and no dome light. Check wiring.

I have the same problem I replace the Gear in in both or my light go to E bay and researcher repair kit for corvette light , if You to know how repair them log again to Fixya .

Here's a link to your lights.

Not a Corvette expert, but I don't think sunlight would have any effect.
The motors should close the doors when you turn the lights off regardless if it is dark or not.
Are the headlights staying on, or just the doors staying up ? The up position is the default when something is wrong, so I think it takes voltage to close them.

There are three round plastic pellets that wear out and turn to powder causing the headlight gearbox to malfunction. They cost about 4 dollars per side, pretty easy fix if you take your time. I just replaced them in my 89 vette. Of course I bought the best brass gear thinking I needed them. The plastic gear was still in great shape, don't waste your money, you don't need the brass gear, They cost $58.00 each. All you need is the pellets, $4.00 on ebay. There is no vacuum on the headlight system

You might have a vacumn hose off or a bad actuator.

http://willcoxcorvette.com/instructions/headlamp_and_wiper_small_parts_function_2.pdf GREAT INFO

I’m happy to assist further over the phone at https://www.6ya.com/expert/richard_9a19ee73dfa4686a

Raise the headlights, either with the switch or manually by turning the knob on the headlight motor counter-clockwise.
Unplug the lights NOW to avoid an accidental closing on your fingers,
Remove the 3 philips screws holding the black plastic surrounding the headlights, and slide it forward, there is a small clip on the top that helps hold it to a corresponding clip at the top of the headlight,
Look inside the cavity and you can see the 5 nuts/bolts ( 6 on later years ) that need to be removed,
If you are on the driver's side you can now remove the whole assembly, on the passenger's side you must first unplug the headlight door control module.

The head light door on Vets are vacum activated it is possable that the hose is cracked or lose and losing vacum.