Thanks for your suggestion. I studied that thread pretty closely, plus other threads dealing with mounting jerry cans and other things directly on the camper. My box is long and skinny, so assuming we're talking about a camper mount, I need some kind of lower bracket attached to the camper to support the box. I believe the upper bracket will bear most of the weight.
Here's another photo/drawing showing how the upper bracket will be bolted to the frame using existing mounting points (from left to right, grab handle, step, and jack plate, 7 through bolts total). The bracket in the photo is a bit too high, but you get the idea. I feel pretty good about the upper bracket.
I think the box has to be either attached to the camper or to the truck, not both, as per So Cal's comment, but I may just have a limited imagination.