Why won't headlights stay on after you turn off the engine?

depending on the engine temperature the fan is supposed to remain on after you turn the engine off, until the engine reaches a preset cooler temperature. when it reaches cooler temperature usually within 5 minutes or so it should cut off... if you cut it off and it is running 30 minutes later.. then there is a problem with the fan relay or temperature sending unit.

Might these be "driving lights"?
Cars with "driving lights" have lights that are supposed to stay on all the time the engine is running.
These lights not only look like headlights, in fact some cars even have the headlights themselves come on when the engine is running. Look as some more (several) 2002 Grand Marquis's and see if they are the same.
Be blessed.

Are you sure that you do not have a delay timer on these lights? This is a feature that keeps the lights on for a set amount of time for you to see your way to the door or whatever. My light timer is on a 30 second hold before turning off.

remote entry wont work because either remote battery is dead or remote broken.cluster light will stay on if head light stay on could have faulty headlight relay or headlight control unit faulty let dealership check it out.

This is a feature for safety. If you turn off headlights before the engine, they go out immediately.
If you leave lights on when turning engine off, then turn off headlights, they stay on for approx 30 - 40 seconds, to allow one to walk to the door etc, with illumination on.

If you mean several mins, then time it to check consistancy. If consistant, may be a program issue, if not consistant, maybe a relay issue.

How long do they stay on. On most of the newer vehicles there is a 'convienance" lighting function that allows you to exit your vehicle and have light to get into the house before they shut off. This is usually anywhere from 30 seconds to 1 1/2 minutes, depending on the manufacture.
If you turn off the light switch before turning off the engine they should turn off immediately.

The motor is fine because it runs. More likely is an ineffective limit switch that is supposed to signal 'open'.

More info please. If it is newer model the headlights will stay on for a period of between 10-30 seconds even after the car is shut off. If the lights stay on constantly for longer than that than it will be a different issue. Post up more info if that is the case.

drive it off a cliff! hahaha

IF THE BULBS ARE OK CHECK THE HEADLIGHT MODULE(IT LOOKS LIKE A RELAY, ORANGE CASE I THINK) TRY WIGGLING IT,IM PRETTY SURE THATS IT. THEY GO BAD ALOT ON SAABS. IT SHOULD BE IN THE ENGINE CONPARTMENT