Or a dead short to ground somewhere between the headlight switch and the lights themselves. I would disconnect the battery and do some testing with a meter. You don't want to keep draining the battery with a short like that if that is the problem.
Disconnect the wire at the headlight end and with the switch off, measure resistance from the headlight end of the wire to ground. Should be infinite resistance. If it shows any resistance below infinite then you've got a short to ground somewhere between the switch and the headlights (or inside the switch itself).
Then with the wire still disconnected, measure the resistance from the switch to the headlight end of the wire. That should read close to zero ohms. Anything more that a couple tenths of an ohm and there's a problem with the wire like corrosion, rust, dirt or a loose connection somewhere.
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