All cars did when they got small enough to fit inside, since it's purpose was to regulate alt output in the first place.
The new alternator probably has a faulty voltage regulator.
change alternator
Put a new alternator on it or tear the old alternator apart and replace the voltage regulator in it.
It's inside the alternator, most people just replace the alternator if it isn't charging but you can take the alternator apart if you know how and put in a new voltage regulator for about $15.
Assuming you are asking about the voltage regulator, the voltage regulator regulates the voltage being put out by the alternator or generator so not to overcharge or undercharge the battery and maintain the correct voltage for the electrical system. In 1964, the Lincoln voltage regulator was externally mounted. In later years it became integral with the alternator.
Most vehicle manufacturers now put the regulator inside the alternator.
To get to an internal voltage regulator first disconnect the battery ground ( negative cable ) then remove the alternator. Make sure you mark the cables on the alternator so you can put them back exactly where they are supposed to go. The voltage regulator is inside the alternator and you will have to take it apart. I'm not sure how the regulator is mounted in your alternator, it might have small studs with nuts on them, or small screws or bolts, or it may be soldered in. In the latter case you will have to cut out the voltage regulator and solder in the new one. If you are going to take out the alternator anyway you should probably take it to a parts store where they will test it for free and tell you if you need a whole new alternator or just the voltage regulator.
bad voltage regulator is a possibility
The battery light comes on when the alternator output voltage is too low or too high. You have a wiring or regulator problem.The battery light comes on when the alternator output voltage is too low or too high. You have a wiring or regulator problem.
Because your alternator's not putting out any juice. It could be the alternator, the belt or the voltage regulator. If it's the belt that's pretty easy--get one and put it on. Either of the other two and you'll need a rebuilt alternator because the regulator is inside the alternator case.
Which regulator? The voltage regulator is INSIDE the alternator. If that regulator has failed you can either rebuild the alternator (don't even try unless you're experienced), or you can simply replace the alternator. The fuel pressure regulator is near the rear of the engine, drivers side. Just get a new one, pop out the old one, clean everything well and put the new one in it's place.
It will be fine as long as voltage regulator is working properly