You have some kind of problem there. And you know what they say..."better you than me"
The gas gauge works based on the resistance of the sender in the tank so I'd say that when you turn the lights on, you're increasing the total resistance so the needle drops but I run screaming from electrical gremlins. Do you have a ground strap from the engine to the firewall? You'd be surprised how many problems I've solved by just making sure there was a good ground.
The first thing I would do is check, with a voltmeter, what the battery voltage is with headlights off, then on. Do this right at the battery posts, then at the terminals. A change here could mean that the alternator or regulator isn't up to snuff. Then, check again with the negative lead of the meter hooked to a body ground (fender, radiator support, etc). If there's a difference between the two readings, then you have a bad ground between the battery and the body. If the reading doesn't change, then move into the car and check the voltage at the instruments fuse, first with lights off, then with lights on. If there's a change there, check the connections on the terminal strip of the horn relay. Make sure they are clean, with no corrosion. Most problems, such as this, are usually caused by bad grounds or corroded connections. Good luck!
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