IIRC.

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Purple is normally asscociated with the Speed Sensor.

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Does the speedo and power steering work?

However, thinking aloud here.

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did you car have factory fit alarm??

The best thing to to is to get a biro and follow the track to where it goes on the back of the instrument cluster.

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it might go to a bulb that someone didn't want lighting, ie.

an Alarm Warning or Security light.

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If an aftermarket is fitted and the factory one is bypassed the lamp may have been constantly on.

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HTH