Unexplained Voltage Drop

I cannot keep my lights on for more than 5 min or so with the engine off or my whole system is dead. My alternator and battery bench tested fine several times. I also took a voltmeter to the system and my alternator was pushing right around 13.75 volts. My battery, while the engine is off sits around 12.65 volts steady. Sounds good, right?

If I turn on my lights while the engine is off and the battery is hooked up, I lose .01 volts every 5-7 seconds. This is true for both the headlights alone, and the fog lights alone. Obviously something is messed up. My car will start every time with no problem if I simply remember to turn everything off.

Terminals are clean and have good connections. Fuses are fine.

Cables? The cables are more expensive than either the battery or the alternator. Hence why I didn't start there.

As always, thanks for all your help.

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Curious to know what the "bench test" of the battery consisted of. It sounds like the battery's reserve capacity is way down from where it should be, possibly due to sulfation of the plates.

How old is the battery?