I would first check all fuses. My 2002 uses a weird configuration and requires several fuses to work all of the lights properly.
The taillights are supposed to go on when the headlights are activated.
How do you install projector headlights on a 1998 Chevrolet corvette
In the fuse panel to the left and below the steering column. The full size trucks have an issue with taillights. These taillights have a circuitboard on the backside of them. They have been known to go bad.
Yes, there is a headlight relay,
Fuse for headlights 1990 Chevrolet suburban is located on the driver's side dash on left right behind the fuse panel. It is just above the parking brake.
sounds like a battery issue
Remove the wiring harness from the back of your 1997 Chevrolet Z71 headlights. Remove the headlight retaining bolts. The headlights will come out. Reverse the process to install the new headlights.
If you respect others then you will go to an auto body shop and have them adjust them for you. I am sure you have had the experience of someone elses misadjusted headlights.
If by convertible headlights you mean the concealed, or pop-up headlights, they first appeared in 1963, and lasted until, and including the 2004 model year. Fixed headlights made a return in 2005 with the C6 series Corvette.
I had this problem and it was a bad alternator.
This information is in the owner's manual. If you don't have one, you can download it from http://gmownercenter.yahoo.com. Push the dome override button three times (in, out, back in). You'll hear the familiar "ding" and the parking, headlights, and taillights will go out. You can then control them using the parking / headlight switch. You can also idle the truck with the lights off by starting it with the parking brake applied. You can also use the switch to turn on the headlights during the day (rain, etc.). Here's a photo of the location of the button under the headlight switch: http://monsterautoparts.com/chevrolet/chevy%20truck/_images_chevy_truck/D1534G.jpg
The 1999 Chevrolet has a separate fuse for the low beam headlights. The low beam headlight fuse, can be found in the fuse box.