The secret weapon of the day is music wire, also sometimes called piano wire. It is a super stiff, hardened steel wire, available in diameters ranging from .006 inches to .192 inches, a range that starts out smaller than a #80 drill, and ends at the approximate size of a #10 drill.
You have to be careful when working with it, because if you try to cut it with a normal pair of wire cutters, you’ll notch the blades. The wire cutters will win the battle, but they’ll be scarred for life. Most people use a rotary tool to cut it. If you don’t have a rotary tool, a fine-toothed saw will work unless you’re using a super-thin size.
I find it especially good for making repairs in thin material. Select a wire size no larger than 1/3 the thickness of the piece to be repaired, and a small drill bit that matches it approximately. Experiment on a scrap piece to find a good match. Drill a hole in one of the pieces. Drill in at least twice as deep as the piece is thick, but longer is better.
Once you get the hole drilled, insert a small bit of wire that fits in the hole but only protrudes out slightly. (You won’t be using this bit of wire for the repair; it’s a sacrificial piece.) Dab a bit of paint on the end, then position the other piece. This marks where you need to drill the other piece. Drill a hole at the mark. Depending on what you’re repairing, you may need to use multiple holes and pieces of wire.
To get the right length of wire, insert a piece of wire all the way in, then mark the end. Measure that distance. Then repeat on the other side. Add the two numbers together, then cut a piece of wire a millimeter or so shorter than the total.
Apply some appropriate glue (something compatible with both the steel and whatever surface you’re gluing–a plastic-compatible super glue is often a good choice) to about half the length of the wire. Insert the wire. If you’re using more than one piece of wire, repeat. Then apply some glue to the exposed portion of the wire, and put the piece on place. Apply a bit of glue to the edge of the piece as well.
The process is time consuming, but will usually result in a repair that’s stronger than the piece was to start with. It will certainly result in a stronger repair than using glue alone.