I have a similar problem on my 54 half ton. I finally installed a quick disconnect. I use the disconnect whenever I park the truck for more than a few hours. I think mine is caused by a faulty generator and a possible drain on the battery.
Stump 1969 C-10 With - 305 C.I. Short Wheelbase - Stepside 1986 C-10 With 350 C.I.