91 vette headlight doors will not open or close

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.

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

the relay for reversing the moter might need replaced

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.

those have a vaccum(engine) operated actuator

lol ok.. you may need to check all of your lights and fuses, not just head lights.. example from experience, we had a 91 firebird that had a tail light out and every time we hit the brake pedal both head lights would come up after replacing the bulb on the tail light the head lights were fixed...

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

if they both stoped workin at the same time i'd start by checking all the vacuum lines going to the headlights