Mystery is why you are getting 12.8 at the ASC and 11.x at the battery itself. Is there another battery source? Truck battery via 6-pin?
Yes the intermittent monitor reading could be from a fault in it. EG, on my range hood monitor that came with the 1991 MH, the rocker switch that operates the various indicator lights was broken. You can buy those rocker switches.
That battery sitting at 11.x is getting ruined. It needs a full recharge ASAP plus an "overcharge" to clear up the sulphation now forming. Without shore power to run a charger I don't know a good way to do that with no solar. Your solar is not reaching that battery, although it might be reaching the truck battery somehow--I can't tell what is going on there from here.
