I currently have a similar problem with my regulator.

The gen light has come on with the engine off and key removed. After a rap on the regulator with the handle of a screwdriver, the light went off. Now and again the gen light comes on when the engine is running, but turns off when the engine is shut off. If I rap on the regulator when the engine is running, the light goes off. All of this happens about every three or four days, but does not act up in-between.

I purchased the regulator in March from Ames. I am going to give them a call and see if they will exchange or do anything. I am convinced the entire charging system is fine, just a bad regluator.

But perhaps you have a different issue with yours. All the connections on my regulator look fine, and I did not hear any relay clicks, but I admit I was not listening for something like that.