2002 Volkswagen Jetta alternator

If you still have 12.8 volts at the battery, why do you say the generator is working? You're right about the charging voltage. Unless the manufacturer specifies something different, we want to see between 13.75 and 14.75 volts.

You can start by measuring the voltage on the larger output stud on the back of the generator. That must always be exactly the same as battery voltage. There is a large fuse, usually bolted into the under-hood fuse box, or a fuse link wire, between the output stud and the battery positive post. If that is burned open, you'll have 0 volts on the output stud with the engine off, and usually real high voltage, like 15 or more volts, with the engine running.

If the voltages on the output stud are okay, you have to look at the wires coming in. I'll have to look for a wiring diagram to figure out where to check next.