The Duramax uses both batteries all the time-- Starting [takes lots of amps] and running. They are wired in parallel. There is no diode in the system.
The trailer terminal is hot all the time, if the wire has been connected, and it has a fuse in the under hood fuse box.
Chevy 04.5 LLY, 2X, shell, XDR, MikeL Heavy duty up-grade, 6spd, TransGo, deep pan, de-badged, 65 Gallon replacement Aero tank, LBZ-mp, Kennedy pump, shimmed, Pre-fuel filter, tow mirrors, BU cam, gauges, GPS, Sirius, bags, custom grille, fender vents, HD trans cooler- Curt front hitch, footwell lights, load lights, Studs, head gaskets.--- Jerry