You need to post the information from the cooling air cowl - the long series of numbers divided into Model, Type and Code - before we can deal with your questions with certainty. The Briggs ignition system uses a "kill wire" which is always black, coming from the system. Whenever the kill wire is grounded, the engine will not fire. However in very old Briggs engines (prior to 1982) the kill wire comes from the breaker points, inside the flywheel. In 1982 and later engines the ignition is electronic and the kill wire comes from the Magnetron unit, a modified form of the coil unit found on the earlier engines, located outside the flywheel.
So, you need to locate the kill wire. We can help you do that if you post the series of numbers, plus you remove the cooling air cowl and post pictures of the ignition module. You have said that you have an electronic ignition - we need to verify that, and find the kill wire coming out of it.
