I have used this technique for many years to quickly and precisely place consistent rivets using wire.  The first step is to lay out where you want your rivets.  Center punch each rivet location.  Then drill holes at each rivet location, Fig. 1.  The hole should be about .001” undersized or the next drill size down.  In this case, I’m using .024” wire so I used a #74 drill (.0225”).  I use a separating disc in a handpiece to flatten the end, Fig. 2.  If you want a round head, then you need to round this end.

Next you move down the wire a bit and, with the disc at an angle, roll the wire against the separating disc, Fig. 3.  This has the effect of putting a point on the end of the pin.  Don’t cut all the way through.  I use a hemostat to break the wire off, Fig. 4.  I have modified a hemostat by removing the normal serrations and cut a lengthwise groove in one jaw to help hold the wire, Fig. 5.  After you break the wire free, insert the sharpened point into the hole, Fig. 6.

I make a punch by drilling a hole in the end of a piece of brass rod, Fig. 8. It doesn’t have to be anything fancy. In this case, I had a short cutoff, but anything will do. The key is to drill the hole one size larger than the wire. The depth of the hole will correspond to the height of the rivet. Also, round the edges a bit so you don’t mar the surrounding plastic. Using the punch, you push the wire the rest of the way into the hole, Fig. 7. Figures 9 and 10 illustrate the result. Once you get rolling, this method is extremely fast. I usually place a number of pins with the hemostat and then quickly go back with the punch and set a number of rivets at one time. The other great advantage to this system is the ability to precisely layout the rivet location quickly.  This entire back plate took about 15 minutes.  I spend longer than that looking for the fuel cap that slipped out of my fingers.