This is a fun brainstorm!! Get yourself a clamp meter. It would answer a lot of questions and do so very quickly and easily.
https://www.amazon.com/s?k=true+rms+clamp+meter&crid=37FBYM7KY9DYE&sprefix=true+rms+cla%2Caps%2C213&ref=nb_sb_ss_ts-doa-p_1_12
From what you wrote my first guess is something like a small light bulb in a door or side mirror is drawing power when you open the doors frequently to grab food. That seems to be the only difference compared to being parked at home.
I would buy/borrow a clamp meter and do this:
1. Open hood and stick your clamp meter on the POS battery cable. With the keys out of the vehicle open a door and see if there is a small amp draw. If there is see how long it lasts. Close the door and see how long until it shuts off. Could be the answer right there. I think a small 1 or 2 amp draw would be enough when the battery is already toast.
2. Start the truck and take note of alternator charge amps. Google what is normal for your model. Then plug in the trailer and see if anything funky changes. I think newer vehicles do not supply a high amp charge for long periods. So like others mentioned it could have to do with showing up to glamis with batteries that were not fully charged during the drive. You could also turn off the truck and measure amp draw with the trailer lights plugged in versus not. If its just 2 LED brake lights it shouldnt be more than 1amp i would guess.
3. If youre lucky enough to catch the mystery load with the key out of the ignition start pulling fuses until it disappears. We had an Escalade that was randomly draining a battery overnight. With no lights left on. Nothing in cig plug. Using a clamp meter and dozens of attempts i came to discover the circuit for the radio would turn on in the middle of the night. Enough to kill the battery. I believe the cause was a dirty fuse plug that was filled with wet looking dirt and grime. The clamp meter was showing something like 1amp draw and pulling the radio fuse stopped it. You might be able to do something similar to trace down where the power draw is coming from.