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Ignition points aren't very common any more but if you've got an older engine you may still have them to deal with. Most Briggs engines can be retro-fitted to electronic ignition but you may choose to stick with the points.
There is one common error when installing new points that gives folks a big problem. Neglecting to properly clean the points before putting everything back together and then wondering why their new set of points aren't working. Yeppers, new points need cleaning to remove oxidation and any oils from handleing. The last thing you need to do before replacing the point box cover is to clean the points.
Cut two half inch strips off a clean, white piece of scratch pad paper. Get a spray can of carb, brake or electronic cleaner. Turn the engine so the points are closed. Soak one end of one strip of paper, spread the points and place the wetted strip between. Close the point and using only the normal spring tension to hold them close, drag the wetted paper through. Do this several times, re-spray the paper if it starts to dry.
Next, get the second strip and leave it dry. Repeat the dragging process to dry the points. On the last drag through, lift the points before the edge of the paper passes. This is important because one tiny fiber of paper tearing off the edge and being left behind can foul the points. I can't begin to tell you how many times over the years that I had to go back and clean new points that a new guy in the shop or the home diyer other wise installed and set correctly. It's the easiest part of installing new points, but probably the most important.