1993 Pontiac Firebird with vibrating headlamp and alarm system that won't shut off.

In regards to the headlamp going up and down on its own that means the motor is worn out or the gears that control the headlamp are burned out you can unplug that headlight and take it out and there is a replacement kit you can buy online for it for the gears and replace the gears or the motor it's one or the other. In regards to your car alarm I would try to trace down if it's a GM factory alarm track down which wires control the alarm Etc and just disconnect them if you don't want the alarm anymore otherwise you might want to take it to a stereo shop and they'll do it for you