If your Briggs motor is very old then it will indeed have contact breaker points, beneath the flywheel. The recoil driving dog serves as a flywheel nut, undo it the normal way to allow you to work on the flywheel. A large adjustable spanner will do this or you can tap the lugs round with a hammer. The flywheel may have 1/4 unc threaded holes to allow you to fit a puller to. When you get the flywheel off, the points are opened by a peg driven by a cam. Replace the points and condenser and set the gap at 15 thou.
John, October 2009