New alternator and batteries still reading 12.0 volts

It sounds like the either the new alternator is defective ( which can happen often) or there may be a possible wire connection problem from the trigger wire or heavy wire on the alternator back to the batteries.
reading 12.0 - 12.04 volts is not charging your batteries.
You need a bare minimum of 12.5 volts ( and that’s to low) to begin to charge a 12.0 volt battery.
Think of it as trying to fill a tire with 40 lbs of air in it to
50 lbs with an air hose that only has 40 lbs.
The tire will never get beyond 40lbs.
I believe from your voltage readings that the alternator has zero output and you are reading the voltage of what’s in the batteries.
When an alternator is charging correctly it should put out between 13.5 volts to 13.8 volts to push voltage in to a battery.
You will need to go back to a TA and have them figure out what the issue is now. ( all should be under warranty in my opinion)
You should get there quick as possible because I believe you are running on the reserve power of the batteries and when that’s gone the truck will quit.
Bottom line is either the New alternator is no good or they missed diagnosed a wiring problem problem from the beginning when they sold you all the parts.

 

Bad power feed to the cab.

 

You may have a bad ground from the alternator to the truck.

 

I've been driving and working on trucks for over 20 years. The connections will loosen up. Positive, negative all of them. Pot holes cracks at 65 mph cause this. Even so much as a quarter of a turn of the nuts and bolts to the connections will leave a weak battery.

 

You should never go to truck stop mechanic

 

An alternator is an electromagnet meaning voltage going into a coil of wire creates variable magnetism. This is called the field coil. The voltage regulator "looks" at the system voltage and "tells" the field how much magnetism to create, in order to dictate how much output to replenish the battery voltage level. 13.4 to 14v is a healthy output and thatll get your batteries up to say 12.6 or so resting. In the old days it was a dang lightbulb in series on the field wire that would burn out and stop your alternator from charging.

As simplistic as it seems that bulb was quite clever. When not spinning, you click the key on and the bulb has zero volts [ground] on one leg and 12v on the other so it fully illuminates which tells you the bulb works. Now start the engine. The alternator produces 13ish volts and now that bulb has the same voltage on each leg so no current flows across it. The bulb goes out. When you had a slight charge issue youd have a slight current and a dim glow on the bulb to tell you of trouble. When the bulb fully lights while engine is running you know the charge just quit.

An alternator that is charging will have a magnetic field around the back side that you can easilly pick up with a wrench or any other piece of metal. If your battery voltage doesnt jump up when you start engine, you arent charging. First look at the field wire. If it doesnt have 12v to the alternator it cannot excite the field to create magnetic flux to turn into volts.

 

I may have missed what kind of truck this was when reading through, but I have had this issue more than once on internationals, they have a fuseable link on the starter solenoid that is the other side of the alternator wire, I’ve seen them rubbed through on the frame. And have bad connection

 

When I test my battery, I see about 12.4 to 12.6 on it. It's adequate. Now when I fire the engine up the voltmeter goes to 14 and change. That tells me that the battery is charging.

Once in a while I have had situation where the alternator quit charging and now I see the volt meter start dropping with a red lamp on it. That tells me Im on batteries and I have about 3 hours to find somewhere to shop it before I drain the batteries so much that the fuel pump will quit working. (Pre computer trucks, air breathing engines) Computer trucks can endure a voltage drop to about 10 pounds and then brick off because it is a miniature computer that cannot stay booted on and functioning at or below a certain voltage, which would usually be at or less than 10 volts.

I don't have much else to offer Except that when you have a good tester that tells you each battery has charge and that the alternator is creating a charge sufficient to feed batteries, around 13.6 to 14 and up. (But not too far up.)

We had a truck once in 2000 that would go close to 15 volts on the voltmeter when shes running at 1500 cruise speed on the highway in the day time. That usually got pulled down when we turned on the inverter and fired up a 120 volt Mr Coffee behind it to brew a pot of coffee. Then she will come down to about 12.8 or so until the coffee pot was finished and turned off. (With inverter turned off) If it had kept falling down past 12 volts and did not come back to where it's normally at, you instantly know you have at least lost your alternator. OR you have at least one bad battery back there in the group.