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I also had similar problems with my 84 GTI. However in my case

the culprit was a poor ground connection from the battery to the body.

The grounding circuits were good enough that the starter could turn over

the engine, but vibrations (usually at higer rpm) caused the ground to

the body to get 'poor' and made the hi rpm light/buzzer come on.

It took a while to find, but my first step, too, was to put a mechanical

gauge in tandem with the idiot lights so I could verify I wasnt frying

my engine.