There are three units to the regulator. The click is probably coming from the point set that's in line with the BAT wire, the cutout relay. The point set on the opposite end is the voltage regulator, in line with the FLD wire. If the spring tension on the voltage regulator points is a little low, the voltage from the generator won't be able to keep the cutout relay closed. Don't fool with the center regulator coil behind the ARM wire- - - -it's the current regulator and it's very rare for it to need adjusting. You might want to clean all the points by rubbing a clean piece of business card stock between them, but DON'T file or sand on the points. Don't allow the cutout relay points to close with the engine off- - - -the battery will short itself out through the generator if that happens.
First, charge the battery fully, then bend the spring anchor on the voltage regulator points up carefully until a voltmeter across the battery terminals reads 14.7 to 15 volts with the engine running at a fast idle. This MUST be done against a fully-charged battery, and the reading will drop slightly when the cover is reinstalled on the regulator. If adjusting the regulator doesn't help the click, you've probably got a dead spot in the generator armature.
Jerry
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Ignorance can be fixed; stupid is forever!