Rivet gun - turns out that I needed to disassemble the head, clean all the oil off the jaws, and re-lubricate the mechanism (but NOT the inside of the jaws!) and it works fine. Excellent customer support from Stanley tools on this thing.
With the rivet gun working, it was relatively quick work to assemble the "skeleton" for the horizontal stabilizer. I also did a test fit of the skin. I tried doing one side (top of the stabilizer, from the leading edge to the trailing edge) then the bottom. Next, I tried doing it from the leading edge down both sides evenly. Doing it from the leading edge seems to work best. I may try working from the trailing edge of one side up and over the leading edge down to the trailing edge of the other side next. One thing is certain, though. It is time for me to figure out if and how I want to put corrosion proofing on the inside, line it all up, and rivet it all in place. Then I can move on to the rudder, vertical stabilizer, and elevator.