Your first pic is confusing. You have the positive (red) DVM lead connected to the negative battery lead. I assume the black lead is on the negative battery post. This setup would degrade the battery voltage by any load your system has including your problem. If all your systems are off, I would think you should read zero volts as the battery should be disconnected from your electrical system. Anything like the radio memory or clock should not drop that much voltage.
I had this problem which was caused by a leaking diode pack in the alternator. Do you know how to check the alternator?
