I dug around in the shop and found a nice long piece of 1x4 fir and a 48 x 30" piece of 1/4-in plywood paneling that looked like it had come off of a packing crate or the back of some piece of furniture. All the edges had water blisters, so I trimmed off an inch all around that dictated the length of my box (46").
I have quite long legs (38" inseam), so the seat sits at the maximum rear position. By poking some 2x4 pieces behind the seat, I figured that if I made the box 12" tall, I could make it 4" deep and still get full seat extension (if you never have the seat back that far, a 6" box would be much more useful).
Here's the project half-way done. The plywood is 46 x 12" and the partitions are nominal 4" (actual about 3-1/2"). I first drilled 5/16" holes at each end of the step in back of the cab near the 2" access holes already there, fed 1/4" bolts up through them and tightened them into place with a nut. Then I took the bottom board (4 x 46"), centered it and spaced it from the back of the cab with the two pieces of plywood. Then whacked on it at the bolt points to mark where they would go. I drilled these to 3/8" for a little slop in fitting and checked to be sure the base piece would fit and the bolts were long enough.
Next, I made a little tool box (center of the photo) to hold my tools. If I could have folded this from sheet metal, it would have had more capacity. I used a 1/2" dowel for the handle, but did not glue it in place, so I could slip it out for easier access to the tools. I put a block on the two center partitions to hold the box so the top was just below the V-cuts in the partitions.
Each partition had a shallow V-cut to help keep my broom sitting on top of the box. The right-hand compartment is 12" wide, the middle one a smidge over the 16" width of the toolbox, and the left-hand one whatever was left.
I glued the other face on the box, tacking all surfaces with a 23-ga pin nailer to hold them until the glue dried. I finished by stapling a scrap of indoor-outdoor carpet on the back of the box in case it wanted to rattle against the back of the cab (it didn't).
The box was bolted in and filled up to look like this. I had room for a first-aid kit, small blue tarp, gloves, and a thin windbreaker in the left compartment, jumper cables under the tools in the center compartment, and some shop towels, rags, ratchet straps and bungies in the right-hand compartment. The broom sits on the top. The box is very solid and a good addition. I still had to stick my big X-lug wrench and a set of retired fan belts (just in case) under the seat. Fire extinguisher in one back corner, a quart of oil and can of brake fluid in the other. It is amazing to be able to open the glove box and not have a lapful of stuff fall out.
Again, if you don't need the legroom, it could have a 1x6" for a base, giving more internal room, and make the tool tray of sheet metal for a little more room. If the seat is always further forward, you could probably add height to the box, too.
Great addition for an afternoon in the shop.
"Old Blue" 1981 F150 Custom, short box, 2wd, straight 6, manual 4-speed; purchased new in NY, now happy in Oregon