Something's the matter with your wiring. A previous owner probably did some repairs under the dash and didn't get the feed wire to the headlamp switch right. It's supposed to be hooked to always-hot +12v, not to ignition-on +12v. This is a safety issue, since you need to be able to have your parking/marker lights on regardless of whether the ignition is switched on. The (usually 12ga red, unfused) wire leading to the headlamp switch's B1 terminal and the (usually 18ga pink, fused) wire leading to the headlamp switch's B2 terminal both need to be live all the time.
(H'mm...did somebody say lights?
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