Seat belt buzzer and light won't go off

Hey guys,
I have a tiny problem with my seat belt buzzer system thing. It was already faulty when I've bought the car. When I sit in the car and turn the ignition, the buzzer and buzzer light goes on, so far so good. Now, If I put on the seat belt, the buzzer won't go off.
Because I didn't care about the dash light in the first place, I've unplugged the buzzer itself but when I drove the car last weekend, the buzzer light went so hot it started to melt the dial.

How can I find out what is wrong? I am completely brain dead when it comes to electric/electronic stuff...

Oh we're looking at a 1974 built Plymouth Valiant base model (VL41C4F *** ***)


EDIT: I've just found out that the buzzer I was talking about might be the headlight buzzer but what's weird is it won't go off either....?

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