I have a '91 Eddie Bauer and I don't know if my answer applies to a 93 model but get an electrician to check your dip/high beam and indicator unit on the steering column. I replaced mine and the problem of no dimmed headlights was fixed. The light switch always seems to run hot with lights on.
Probably a short SOMEWHERE. You have to trace the wires to find it.
This is a wiring issue. If the switch were the issue, the light would not turn on at all. Sounds like something is wired backwards, or there is a cross short. If there is a short to ground, you will be blowing fuses and possibly burning up relays. Consult your vehicle's wiring diagram to ensure the aftermarket headlights are wired correctly.
The car has automatic headlights....they go on and off when it gets light or dark out...they will also stay on for up to 3mins after you shut the car off depending on how the twilight sentenal switch is adjusted. And to take out the headlight switch in the door you have to take apart the door pannel
I would check the rear bulbs. I just had this issue and it ended up my brother had used the wrong bulb, and odd enough it caused the brake lights to stay on with headlights. When headlights were not on and you applied the brakes the dash would light and brake lights worked. Strange, HUH? I must admit before this revelation, I replaced headlight switch and brake switch, with no avail.