Steel. Measures .750 x .380. Slot is .375 x .072
Use a 1/16 inch pin, that's a common size and can be found anywhere. Cut a small portion of it and file a point on one end. Then take a small ballpeen hammer and with the peen end upset the other end. It doesn't need to have a large upset, just enough to sorta roll the edge over.
Now, using a 16th inch drill bit drill two holes in the inlay, do it on a drill press. Using the wedge to hold it in place drill the corresponding holes through the inlay and into the stock, don't drill far. Use the pins to hold the workpiece steady and inlet the inlay. When you are satisfied Use the pins that you've upset and drive them in. Precalculate the length of the pins, chances are you may go into the barrel channel so put the barrel in, the barrel will deform the end of the pins if this happens. The upset end of the pins will draw in the inlay and kinda swedge into the holes drilled. Use a file to file everything flush. If so inclined, put a bit of epoxy in there.
This is the procedure I use when installing inlays and I did a tutorial procedure of it. Good luck.