The process is straightforward; remove the 2 mounting screws and pull the marker assembly out. The lamp itself is socketed in a turn-and-lock assembly. Twist counterclockwise to remove. Replacement lamp for the 93-97's is a 1157LL in the rear and a BP194 in the front.
There's a 30-amp fuse for the headlamps - check that first. Under the hood on the passenger side. Right next to it is a relay that drives the headlights.
98% of the time that's a corroded ground wire for the headlights and I've dealt with it several times. Look under your brake booster and you'll see a flat white rectangular plastic case with about 6 black wires running into it. It's fastened with a #8 bolt straight down into the car chassis. Because it's sitting on the flat shelf it gets wet and once the connectors get corroded, it creates exactly the problem you describe.
It can be opened up and the wires cleaned. There's a good YouTube video that shows how to clean corroded and oxidized wiring in cars:
Use a hose and set the water spray for a high pressure. You can spray it with fantastic cleaner first, if there is any oily residue on the evaporator. Let it soak in for several minutes.
if this alarm was fitted after the car was made then these wires will make connection's to the vehicle's wiring 'you wont find a matching connection, just trace the path of these wires and i expect you will find that where they connect it will be where ONE wire has been cut and each end connected to the alarms wiring ie to cut the power to the injection/fuel pump to stop vehicle being started,one of these connectors will be for power supply and earth so check with voltmeter first then trace and dissconnect, a bit of patiance and all will be good keep me posted if you wish
Batteries may need changing in your key or maybe there is interference from a nearby source, remote control model air craft, if unresolved, have your code changed at dealership.