1996 F350 dually 7.3 XL

Truck's dual batteries will always be dead in the morning even after charging them up and running the truck around some the previous day. Voltmeter in dash shows charging is happening, and verified that there's around 13.6 volts at both batteries when running.
Batteries are new.
I used my voltmeter and noticed with everything off, I was getting a pretty significant current draw (don't remember the value, but will get a small spark when attaching the battery clamp to the battery's terminal) measured between the positive battery post and the smaller gauge wire that comes off the positive battery clamp that I presume runs the electrical system.
I unplugged all fuses and circuit breakers under the dash, and got same current draw.
I put the fuses and circuit breakers back and removed everything from the power distribution box under the hood, and got same current draw.
I put those fuses and circuit breakers back and then disconnected the alternator and got the same current draw.
What else could be killing the batteries overnight? There are no lights or anything left on.

 

Try the glow plug relay, it's up on top of the motor,under the cover,if you still have it on there. You might also want to try the 7.3 diesel section.

 

Perhaps try disconnecting the starter and see if that makes any difference. I recently had a starter that seemed to have somewhat internally grounded itself or something weird causing a power draw. Replacing the starter resolved the issue.

 

What DPD said, the starter internally shorting out. Or the wire to the starter has rubbed off the insulation and is grounding to the block or some other chunk of metal under the hood.
If you've removed every fuse, I'd be looking between the battery and starter. Or the solenoid itself.

 

* Alternator
* GP relay
* POSSibly starter

Disconnect all, then reconnect one at a time until current draw appears.