You need to make sure the truck is charging your batteries... You should read 12.6-7VDC across the battery terminals for a fully charged battery setup with out shore power running (not 13.2VDC as you listed)
Then when you start up your truck this DC VOLTAGE should jump up to 13.2VDC to 13.6VDC telling you the alternator is charging your batteries.
Like the others on here have stated your DC CHARGE from the truck through the small 7-way charge connection will probably only give you around 6-8AMPS of charge current...
That is just a tad more than trickle charging...
Roy Ken