To make the bulb in the dash light up you need a positive and a negative feed.

The bulb in the dash has a positive feed on it from the ignition switch, when the alternator is not running it gets its earth feed via the little alternator wire mentioned above.

When the alternator is spinning and producing current the regulator pack sends positive volts up this wire so you have two positives at the bulb.

Thus 2 positives and no earth at the bulb makes it go out.

You are getting earth leakage up the wire to the bulb which means your alternator or regulator is not functioning correctly, and will need to be replaced.

HTH