The "tiny wire" in the 7-pin in the truck's wiring has enough ampacity for the 30a draw of the 20a charger. The issue is really the voltage on it tapering with whatever is going on with engine battery voltage, alternator heating, and all that.
I expect it will work ok using the 7-pin with the camper. I also am using the behind the cab 7-pin, not the bumper receptacle so that makes the wire a few feet shorter. (Truck has both 7-pins fitted OEM)
The camper's 7-pin wiring is maybe two feet in my case. With a trailer, you have to add whatever more it is in the truck for the bumper receptacle and then however long the trailer's 7-pin wiring is back to the trailer's battery. That could choke some of the amps besides the amps reduction from the voltage drop at the truck's battery soon after you start the engine.
Whatever works in each set-up! I tried running fat wires back from the truck's battery to the box for an inverter set-up and could not find a good route past the firewall. Going under and back up behind the cab got the wires too close to hot things and one got its vinyl covering melted some. :( People do that somehow, but I gave up. Didn't need it anyway.