Confused

OK, first thing is to make sure the battery is actually hooked to the alternator

With the engine off, use a test light or better, meter, to ground, and the positive probe on the big battery (output) stud on the alternator. Should show same as battery voltage.

Next, turn on the key, and identify which field (push on) terminal is hooked to switched ignition (blue in a stocker). This too, should have "battery" voltage.

Now disconnect the remaining field "push on" --the one going back to the regulator-- (should be green in a stocker) and put your test lamp from the exposed terminal to ground. It should light, showing you are getting "switched ignition to the field, through and "out" the field.

The regulator then controls "ground" on this second terminal to regulate.

Next, make sure that the ignition terminal of the regulator is getting battery, and MAKE SURE the regulator is grounded.

If all this looks good, "full field" the alternator (bypass the regulator)

On your diagram, unhook the bottom field connector (marked --) and GROUND the exposed alternator terminal. With the key on, there should be a small spark as you do this, indicating the alternator field is drawing current.

Start the car, and slowly increase RPM The ammeter, if used should go up, and if you are monitoring the battery with a voltmeter, the voltage should climb. Be careful, as you have no regulator. Try not to let the voltage go above 15

If none of the above works, you probably have a bad alternator. Pay attention to "does it spark" when hooking up the field / key on. If no spark, you probably just need to replace the brushes, a cheap fix

IF this works, you have regulator problems. Recheck the regulator wiring. Try jumpering across the two wires in the regulator connector and rerun the above test. If that works, probably the regulator is DEFECTIVE ( "New" does not mean "good.")