Well i just purchased a 93 GXE w/ 89,7xx miles. The car has been garage kept for 11years and has been parked for the past 2 1/2 years, and i just got it today and as it was turning dark i turned the headlights on and only the driver side turns on, but when i put the high beams on both come on.

so i went and bought another bulb and replaced the pass side but still the same reasult, so i checked the fuse and that was good so idk? and when i turn the headlights off now the driver side stays on even with the key out

 

Gonna have to pull the steering column covers off and look at the light switch assy. It comes out pretty easy. You'll need some small screwdrivers to get the back cover of the assy. apart. Look for corroded contacts. A Dremel with brass brush tip works great.

 

I'm pretty sure that it's your headlight switch, I had the same problem and failed my state inspection because of it. I went to a junkyard and bought one (inadvertently had to buy a whole damn steering column though).

 

^^Ditto^^

 

I took my switch out and cleaned the contacts and problem was fixed. But that was only after I had said screw it and wired a relay off of the driver side to bypass it because I didnt have time to research it. Becareful not to bend the contacts and you should be straight !