One of the wires on the three cavity connector should remain energized at all times. Depending on the year model, this color is probably orange with a light blue tracer.
How fast are the batteries drained? If it is overnight and the next morning the truck won't start, then you can try this test: Charge the batteries or operate the engine until the batteries are fully charged. Then allow the truck to cool to ambient and the batteries drain - minimum of 12 hours. Then put your hand on each battery and the alternator and feel for temperature differences.
Killing these batteries overnight takes quite a drain. The energy will be dissipated as heat. Not many components can handle that kind of current without damage, so check the big ones first. Frequently, we see batteries that remain warm to the touch until they are drained from an internal short. In the truck, an internally shorted battery will drain the other battery too, since they are connected in parallel.
Isolate the warm component, recharge the batteries, then check again after 12 hours for a drained battery...
