In my trailer the white wire going to the battery is the ground, and the red goes to the positive terminal. My trailer only has one battery, though.
It's hard to diagnose from a distance, someone might have added a battery isolator/switcher etc. etc. Is yuor installation factory, or does it appear to be a modification?
Basically, can you trace the white wires and see if they are indeed the ground?
Remember, just because it's like this in my trailer, does not mean it has to be the same in yours.
You can trace the grounding by using an Ohm meter, commonly found as part of a multi meter. You can also visually trace the wires and see where they go to.
Use caution,
12V can easily burn wires, and trailers.
My best guess is that the red extra wire connects the two batteries in parallel, which keeps the voltage at 12V, but gives you twice the amp hours ) longevity) If both the white wires go to ground, then the red wire would connect the two positive terminals, paralleling the batteries.
But before you do this, take a close lok at things. I am not aware that 69's had dual batteries from the factory, so this might be a previous owners idea of battery wiring.
Be safe!
If in doubt, post some pics of the wiring.