In addition to what Barry mentioned also check the terminal box for a bad connection. With the car off, turn on the headlights. Set your multimeter to measure the lowest DC volts and connect the 2 meter leads to the 2 terminal box wing nuts. You should measure no volts. If the meter measure some voltage or if either stud gets warm it indicates a bad connection at the studs or the amp guage.
As Barry mentioned, I've also seen alternators with bad voltage regulators.