My apologies. Not many "authorities" on here, mostly opinions, many of which need to be taken with a grain of salt.
I couldn't find a load inflation table for your particular tire, but any tire chart of the same size and load index will work.
For a rule of thumb, you got E load tires presumably......since you didn't post the size or tire rating, probably like a 265/275-65/70-17/18.
Empty pickup, 35 psi rear is sufficient, so like maybe 1500lbs per tire actual load, but the tires are good for 2000? Lbs at that pressure. Full load on tires = 3100-3400lbs per tire at 80psi.
If you're at about 2500lbs per tire with your tongue weight and a cooler full of beverages in the truck bed, plus some firewood, etc, doing the math will put you in the 60psi range
That's about as authoritative of a response as I can muster with the info given and not looking at a load chart.
After well over a million Windshield miles in pickup trucks, towing and hauling whatever you can think of, for E load tires, standard LT pickup tires, I run 35-45psi empty depending on the weight of the truck. 55-60psi towing or hauling reasonable items, stuff that puts a ton of less extra weight on the drive tires and full 80 psi when hauling a 2 ton camper or a loaded truck with a substantial tongue weight. Never really calculated it but if the tire isn't bulging it has enough air and when loaded it's better to be over the min psi for the weight than under.
Hope this was helpful.