I have a 1998 firebird formula. When I turn the headlight switch to parking lamps, the headlight pop up. Also when I lock the car the head list pop up. Whenever the hied lights close they make a grinding noise for about 20 seconds. I am looking for the possible cause and fix to these problems. Thank you.

No relay, just old school high current switching including the multifunction switch. There's a "Park Lamp" relay for turn signals and park lamps which the GEM (BCM) module has limited control.

they are dual filament bulbs so the tail light filament might have blown and not the stop light , replace the bulb to check

Check out "Headlight Fix for the 4th Generation Firebird/Trans Am" (http://www.bfranker.badz28.com/headlightfix/).

Park, Tail, Marker Lamps, and License
The park, tail and marker lamps, including the license lamps, turn on when the headlamp switch is placed in either the PARK or the HEAD position, or anytime the headlamps are requested. The RT I/P #1 fuse in the RH I/P fuse block supplies battery positive voltage to both the park lamp relay switch contacts and to the park lamp relay coil circuit. The park lamp relay coil is controlled by the body control module (BCM). When the headlamp switch is placed in the PARK position, the BCM energizes the park lamp relay coil control circuit.
Current flows from the park lamp relay switch to both front and rear park lamp fuses and to their respective park/tail lamps. The front park lamps are grounded at G101. The rear park lamps are grounded at G302. The license plate lamps are a part of the rear park lamp circuit and are grounded at G302. The inadvertent power control feature prevents the park lamps from remaining on more than 10 minutes if left on. If the park lamps are turned on after the ignition switch has been turned OFF, or is in the ACCY position, they will remain on until turned off or until the battery runs dead.

Did you the REAR PARK LP fuse 15 amp in the right insturment panel fuse box.

I think you have a bad shorted battery or bad alternator.

Check all the grounds for the running lights

This problem is caused by the headlight gear being stripped. If you go on ebay, there is someone who sells brass headlight gears. Once you put the gear in, you will not have this problem again. . . unless the other gear goes bad. It's usually the driver's side headlight that does it.

You have a short in your electrical system or bad ECM.

you could have a blown head lamp fuse , bad earth at the head lamps or the switch could be u/s what sort of car is it

You have to take off the bumper to get access to head light