It looks like I won't need to replace the generator, which is good, because it's a pain in the ass on an aircooled VW.
That's because the generator and cooling fan are on the same shaft, powered by the engine's single fan belt. The cooling fan is inside the fan shroud, the large black metal housing on the far side of the engine in this photo:
That's why one of the VW Beetle's two idiot lights -- the red one, no label -- signifies either lack of charging or lack of cooling or both. If the fan belt is intact, it's unlikely to be a cooling problem. But if the generator is hosed, you have to remove the fan shroud to get it out, and given the tight confines of the VW engine compartment, it's a pain in the ass. It has to lift straight up, and as you can see in the above pic, the decklid ("hood") and hinges are right there above it.
I had the red-light-on problem and it wasn't the fan belt, which means either the generator or voltage regulator (box on top of it) were faulty. Reading up on the various tests (I recommend this resource or this one, though the procedures in Muir and even Clymer are adequate*), I decided to try polarizing the generator, since the car had been sitting for several years.
You're supposed to do this when installing new generators, too, but I never have. I've replaced a half dozen or so over the years. I was just lucky they had some residual polarity from factory testing, I guess. It's an amazingly simple procedure that invokes the mysteries of electromechanical engineering: take a device that is normally spun to produce electricity, give it some electricity, and it spins like an electric motor (you have to remove the fan belt so it's free to turn). That "seeds" the generator so it can do its thing. And if it doesn't spin, that's a sign that the generator is faulty.
Took a few minutes to get that big nut off the generator pulley, which requires a potentially knuckle-busting application of socket and screwdriver, thus:
As usual, judicious application of PB Blaster, a few taps of the hammer, and a cheater bar were persuasive.
I then hooked up my jumper wires per procedure and the generator began to spin! So I buttoned it all up and fired up the engine -- not really expecting something so simple to do the trick -- et voila! Red light off!
On to the next item on the list: turn signals and horn.
*of course, I also have Bentley and Haynes. I'm pretty well manualed up.