You have a dead short or a bad battery. Don't go adding solar just yet to a system that is not working properly. You'll only confuse the situation.
You've only given one voltage which is good, running. That should be about 14.6 as stated. Usually it will sit about 13.2-13.4 while running but your alternator is working hard to put juice back in this compromised system.
11.3 after sitting overnight should be about 12.6 or 12.8 to 13.0 if absolutely nothing is drawing power overnight.
11.6 after a few minutes of running (with van turned off or still idling????)
That is very bad. Pull both batteries and have them tested, or if this isn't convenient just pull BOTH leads (pos and neg) off both batteries still in the truck and let them sit overnight. See what your base voltage is the next morning.