there would either be a short to power in your switch / a short to power in your wiring somewhere between the battery and the bulb . somewhere in there electricity is constant and completely cuts out the selector switch. the lights turn off when you disconnect the battery because that is the only time that power is not applied to the bulbs.
Maybe you'd like to explain what you mean. I can't believe you actually want your headlights to remain on all the time - you'd flatten the battery.
sounds like a bad light switch.
Cars don't turn off completely, they run on battery power. The headlight switch needs to be turned off.
Sometimes an alternator with a weak diode(s)can test out fine, but can still trigger the light. I believe the problem is in your alternator. Good luck.
Turn the ignition key to the accessory position which is normally counterclockwise. Only the radio will be drawing power. If you have a good battery you could listen for a couple of hours without running the battery down. Any longer and the battery may go dead. Make sure that the headlights are off; these may still remain on when the key is in the accessory position. Headlights will drain the battery very quickly. It may also be advisable to run the engine for a few minutes every half-hour or so, to recharge the battery.
The headlights require a vacuum to operate down. If there is no vacuum they remain in the up position. You may have a vacuum leak such as a disconnected or broken vacuum line. I have also seen the vacuum reservoir can rotted out and unable to hold a vacuum.
Ruin the battery.
The life of the battery. You never have to change it.
I had this problem with my 1994 Buick LeSabre and it no longer happened when I installed a new battery. It's been at least 6 months now with no recurrence of the problem. Before the new battery, I noticed that if I waited about 5 minutes after turning off the car, I could get the lights to turn off. Seemed like something had to cool down.
you probably have a bad headlight switch.
Had this problem on a 1995 JCL, it was the DRL (daytime running lights) module. If you're lucky yours will cost $100, mine was $350. It was located to the left of the steering column and over a metal plate (white box) completely hidden from view. Do not buy Jeep, they are electrical problem prone and nightmares.
You can bypass it by removing the three pin plug from the lock cylinder. This will only be successful if done while the engine is running. It will remain in "code accepted mode" with wires disconnected at this time and no new inputs! This proccess may or may not need to be repeated if battery power is lost.