I have a 2006 F350.
I live in NC where we had a recent cold snap.
I ran my battery down while trying to get started. (Forgot about my block heater )
When I went to charge the batteries, the second had a full charge.
In my profession, I would give it vitamins!!!!

 

You have a problem, both batteries should drain evenly. My guess is the ground for the second battery is bad.

 

Thanks for your reply. It gives me a definite starting place!!!