[JABURKHOLDER]

I agree that you need to weigh your truck fully loaded for a trip. Full tank, hitch, passengers, tools, etc.

Now the part that hurts, math.

Forget for the time being how your truck is equipped. This is solely based on the numbers you provided plus some basic facts.
Your trucks cargo capacity is based on the trucks curb weight and GVWR. The manufacturer has determined that your trucks curb weight is 7993 lbs. Subtract that from the GVWR (12400 lbs) and you get your 4407 lbs on your tire sticker.
Curb weight does not include people, full tank, hitch, pets, etc. I assure you, your truck will not weigh 7993 when loaded up for a trip. I don't know your fuel tank size but let's assume it's 37 gallons. Eight lbs/gal for diesel gives you 296 lbs. Now your truck is up to 8289 lbs. Let's add a hitch, 100 lbs. Now you are up to 8389 lbs. Let's add people. Two people, 300 lbs ?. Now you are at 8689 lbs. I have not added pets, tools, bed cover, bed liner, etc. and all the extra stuff folks fill all the cubbies with. Your truck will probably weigh closer to 9000 lbs. For now let's stick with the 8689 lbs. Subtract that from your GVWR (12400 lbs) and you are left with 3711 lbs of cargo capacity.

A previous poster used your RV's unloaded weight for their math. No one travels with an empty RV's except for transporters. So it is unreasonable to use that weight to determine pin weight. Personally, I use the GVWR of the RV to determine the MAX pin weight I will ever have. A fifth wheels pin weight should be 20 - 25 % of the RVs weight. Typically it averages out to around 22%. I use 25% for my math as this automatically gives me a safety cushion as I will never load the RV to its max. In your case the max pin weight would be 4000 lbs. (16000 x 25%) That 4000 lbs exceeds your 3711 lbs from the previous math. Not good. Right now you are saying "I'm not fully loaded like that in the RV". You are right. You will probably be closer to 14000 lbs. So, using 14000 lbs, your max pin weight will be 3500 lbs. Congrats, you are under the trucks remaining cargo capacity, but not by much. And that assumes your truck only weighs 8689 lbs loaded.

This is math that can be done before any purchase is made. Doing the math afterwards usually results in disappointing numbers and a scramble to figure out where to cut weight.

At this point, you need to weight your truck fully loaded. Weight your RV loaded for a trip. Weight the two together.

Personally, I believe you will be right at the limit or over.

JMHO based on the info provided.