My generator light is on on my dash. I hooked a volt meter up to the battery and got 12.6 volts with the motor off, 13.6 at idle and 14.0 at 1100rpm. So i think the alternator is fine. What would cause the "Gen" light to come on? I replaced the alternator over a year ago and I haven't had any problems other than this.
The generator light might come on for one (or more) of the following reasons: 1) faulty ground wire of generator 2) faulty voltage regulator (given what you've stated in your post, this doesn't seem likely) or 3) the little blocks ("brushes") inside the generator are worn down. They're the flint-like square/rectangle blocks inside the generator that spin and make contact at preset points inside the generator. Hope this helps.
The light used to come on on my 75 Electra with an 80 amp aleternator. It wasn't visible during the day but was visible at night. It was caused by a bad diode. I had the diode trio replaced and the problem was corrected. A friend of mine had the same problem (GEN light coming on dimly) with a 59 Cadillac but this car has a generator and an external regulator. In this case, the light would come on brighter as the engine speed increased. It was caused by a bad engine ground. I also had this problem with my 68 Wildcat but the alternator didn't charge at all and the "GEN" light was bright. It was caused by a bad (external) voltage regulator.
Gen light If the Alternator is an internally regulated unit and the light goes out when you rev the engine slightly, It will be the diode trio. Easily tested with an ohm meter. If externally regulated the problem sounds like a poor ground... probably at the regulator. Clean the mounting and terminal connections. HTH Good luck!
You didn't say that you replaced the voltage regulator. If it's the original contact type, try cleaning the contact points inside. If it's the solid state type, it's probably toast.