As I remember, that box in the bed side was called a "cargo door" or an "Avenger Door" because it was an option under the Avenger truck package.
I've only see a couple trucks with them still intact, but I saw a lot of trucks with holes where they used to be. Seems they must not have held up very well. I don't believe they were very deep, maybe 6" front to back. I believe they sat just below the bed floor, and any support past the bed side likely came from the bed floor.
If I was going to do something like this, my biggest concern is keeping the stuff in the box dry in wet weather (and winter salt). Every time the truck is in reverse, that area the box is in is subject to whatever the rear tire throws at it, and everything below what ever inner fender, all the way to the ground, is present is game to end up in, at, or on that box tucked inside of the bed's outer sheet metal.
With that in mind, I would want the box attached to the truck frame (like running boards used to be attached), with a splash guard starting behind it (from the bed floor), down the entire rear side (between the box and the inner fender) ahead of the rear tire, and extended the entire length of the bottom of the box. By theory, the box could extend from the bed side all the way to the frame rail, and from the front of the bed to the rear inner fender in front of the tire, but the reality is the box size will be limited by the weight it will be hauling. I suspect the reasons the failure rate was so high was because the box was often overloaded.
Years ago I when I built my 50 Dodge 4x4 (a 50 cab on a 77 1/2 ton Dodge 4x4) I added a box above the running board on the passenger side, but under the cab. It was 6" high, 24" long, and sat on the angle iron framework the held the running board. Even with it being protected on all sides from any water splash, the inside of that sealed steel box was always wet, and quite useless. In the picture you can see the door for the box. When I redid the truck a few years later, I removed the box.
