Tow/haul has nothing to do with alternator output.
If you want another battery in the house bank (camper) but located in the truck, conceptually it's simple.
You'll need about 60lf of 2 or 4 ga wire. Check the drops but 4ga is probably plenty considering you won't be pulling large loads.
Hook the existing house bank to the new battery (in parallel) with the proper lugs soldered on etc and a winch plug to disconnect between camper and truck.
Now you have to connect it to the vehicle/charging source.
(Btw once you're done with this, the little 12v hot wire in the trailer plug is pretty useless for the camper.)
I would simply parallel off the start battery through an ACR/VSR like a Blue seas model used primarily for boats.
This will link the house bank to the start battery and alternator when charging voltage is present, vehicle running, and automatically disconnect once the system voltage gets below 13v or something. Basically when the alternator is not pumping out charging voltage.
From there out, it's completely hands off save for plugging the camper in.
The downside to this is when you don't have the camper on, that one house battery stuck on the truck will be charging all the time, although it will also act like dual batteries for the truck when the truck is running.
