I am sure you know this, but thought I'd try
P0625 - Generator Field Terminal Circuit Low

Description: The powertrain control module (PCM) monitors the generator circuits and sets this DTC when the PCM detects a concern.
Possible Causes: •Charging system

Diagnostic Aids: Verify the battery voltage is 14.5 volts. Verify the generator/regulator has the correct part number.
Application Key On Engine Off Key On Engine Running Continuous Memory
All Refer to the Workshop Manual Section 414-00 Charging System - General Procedures for diagnostic procedures.

 

So what's that man in laymans terms. Check the alternator?

 

The field wire is what gives the alternators electro-magnetic coils energy to operate from the batteries. Once the alternator is spinning it should power its own fields for the most part.
It could be giving that code because there is no power to the field wire (wiring problem), but it could also be a bad field coil (bad alternator).

If you have voltage on the field wire when the engine is not running then its probably not a wiring problem, just a bad alternator.

 

You can take the alternator off and have it tested, chances are it's good. Reason I say that is while idling it should be putting out 14.4,which you verified. But a battery fully charged is actually in the 13.2-13.4 range, weird I know. I had the same problem when I learned all this except my alternator was bad. I thought it was the batteries. What I think is happening is the batteries are holding enough to start, but it's draining them enough to throw the light. And only recharging back too the 12.53. I know without a doubt at idle the alternator charges 14.4. That leads me to believe it's the batteries

 

And it could just be one battery bad and pulling the other down, only way to tell is to pull both charge and test. In the truck they are basically one battery so one will pull the other down.

 

Ok so my truck sat all night last night and all day today. Without starting it, I tested the batteries again. Yesterday I saw 12.53v. Today I'm seeing 12.23v. Temperature last night was in the single digits and today only reached like 20 degrees. Does this help at all in leading me to a solution?

 

Update. Just put two brand new batteries in it and the light came right back on. I guess my next step should be an alternator?

 

Yeah that's the next step, FYI, it has to be on oem alternator or the light will stay on all the time. I would have it tested before I replaced it

 

If you have over 14 volts at idle it is charging but the light will come on under 3 conditions. The first being the output voltage of the alternator is lower than or the same as the battery voltage. The second is that the field coil voltage is lower than the battery voltage. Third would be alternator output too high.

There are two sets of diodes in the alternator. One is a fullwave bridge rectifier with 4 -6 diodes. The other is a halwave rectifier, one connected to each stator coil. The 4 or 6 diode set charges the battery, and appears to be working. The stator diodes provide voltage for the field coils and the alternator light. One of those diodes are bad or the wire to the field coils is nicked or burned.

Check the voltage at the fields (i think its an orange wire with a green stripe but dont recall for sure). If you have voltage there with key on the engine not running, then your harness is ok. If you dont, trace back the wire in the loom looking for a cut or burn. If all thats good start the truck and unplug the connector from the alternator, then check for voltage on the field wire pin on the alternator. It should be zero or an erratic voltage bouncing all over the place indicating a faulty diode from the stator, bad regulator, or a burned stator coil. Since you get over 14 volts output im bettin the coils are fine but a bad diode.
You can of course take it off for testing, and if your harness is good theres something bad in the alternator. But thought i would save you the trouble if its just a bad wire. Im only suspicious of a bad wire becuase you said the light was on, then went off later and came back on. Bad alternators can do the same thing though.

 

Update/conclusion: decided to drop my truck off to a buddy that has a shop, since I didn't feel like laying in a snowy driveway in single digit temps to check it out. So he took a look at it. All wiring was fine, so he did some digging on technical specs of the alternator and he found that at idle, with minimal load (heat off, lights off, etc.) it should actually only read mid 13's volts. So it seemed mine was over charging reading 14.4v at idle with minimal load. So we got a new oem ford alternator, threw it in, and battery light instantly went off and all is good. Thanks for the help and hopefully this can help someone else.

 

THANKS!!! For the update... This will be a help to many 6.4 guys.

 

Ok. So another update. Drove my truck and now the trans is wierd. I have a fully built trans, and am running innovative tunes. Tried reloading the tune and driving like 30 miles and it's still wierd. From a red light, very gentle acceleration, shift from 1st to 2nd is fine, shift from 2nd to 3rd was fine, but 3rd to 4th it either whines out or bucks. Any ideas what's going on?