It's likely to be in the alternator; the light comes on when the voltage from the alternator's field coil drops below the battery voltage, indicating there's no charging output. Since yours is faint, and not completely on, you have a lower output, but it's probably still charging. If you do take it to a parts place to test, you just have to have them hook up the pulley to spin it, and then they have to momentarily apply 12V to the D+ (field coil) input, the terminal with the push on connector. Then the alternator gets field current, starts charging, and is supposed to supply its own field current through internal diodes. I was able to test it myself, using my impact wrench to slowly spin the pully up to speed using the pully nut, (so as not to overtorque the nut), and then, tap a wire briefly to the D+ terminal, to start up the charging process. The drag on the pully is incredible, and this is without any load on the output; the pully starts slowing up immediately, and I can't really keep it spinning with the impact wrench without it starting to hammer. Testimony to the keeping your electrical load down if you want optimal MPG and power.
You should see a higher voltage at the field terminal when the car is running normally, about 14.15 volts or so. The regulator regulates the battery voltage to 14.0 volts, which I think is a bit too high, and may be the reason for the Scorpio's frequent battery fails. If I were so inclined, I'd try to find a way to drop the regulated voltage to 13.8 or so. Anyone ever played with the regulator/brush assembly to try this? Quoted about $38 from Ford for that assy, by theway.