Both the GVWR and the GCWR are calculated when the tow vehicle is designed. Thus the maximum weight of a pickup (GVWR) and the maximum the pickup plus it's trailer can weigh (GCWR) is determined when the pickup is designed.
If the pickup is lightly loaded this will increase the amount it can tow. The maximum the trailer can weigh is the GCWR minus the "actual weight of the pickup" (GVW). (Substitute whatever you want for "pickup" in the earlier statements).
If no GCWR is provided by the manufacturer of the tow vehicle, this implies they didn't intend or think about anyone towing a trailer. We know this is not entirely true because they installed a trailer hitch. That being said, I would honor the GVWR, keep the weight of the Mallard within that.
Then honor the hitch rating and don't tow more that 5,000 lbs.
Keep in mind the extra weight will slow you down on hills.
2002 35R Southwind, W22 8.1L Vortec UltraPower, 19.5' wheels
Toad: Wrangler, lifted and on 35" tires