before you pull the alt off some simple testing well would help.
Just put a meter on the battery to check available voltage. Then start the car. I'm not trying to sound too simple with this but....If the voltage doesn't go up then you can just about bet money you need an alt. If the voltage does go to the 13's or low 14's then turn on all your acc. blower motor, headlights etc. The voltage might drop at first but should pick back up.
The way to test an internal regulator IS NOT TO PULL THE BATTERY CABLE OFF WHEN ITS RUNNING!!!!!! People tell me this all the time. If I would have ever mentioned that while I was sitting in ford school I would have been smacked.
Disconnect the 3 wire connector if you look on the connector or on the regulator you might see the terminals labeled A, S, B.....I think. Connect a jumper wire from the A side of the connector to the A terminal on the regulator. This elimantes the regulator and the gauge....the gauge most likely can't handle whats about to happen. Now connect a jumper wire to ground and then find a screw near the middle of the regulator that says F or ground here. With the car running running ground the screw and watch your voltmeter. If the reg. was the problem you should have about 18 volts at your battery now. Ford says don't do this for more than 5 seconds.
Recap.
1. Put a voltmeter on battery
2. disconnect the 3 wire connector and jump across the A terminal
3. Ground the "F" screw on the regulator for 5 sec. or less.
4. Watch volt meter to go over 15-16 volts and I've seen nearly 20 volts at the battery.
I worked at autozone for 4 years and have seen their testers say all kinds of wrong things on alternators that I knew were good otherwise. So you might be better served to just put a regulator on your alternator if my test proves thats the problem. All you have to do for the regulator is take the belt off and swing the alt. up and install the reg. Sometimes you can even get to it without moving anything.
Lastly just because you recently replaced the alt. don't count it out.