Do you mean the high tension wire? That is a part of the "Armature - Coil", Item 333 in your Illustrated Parts List, and Part Number 298502. You can easily buy a new one, from the Outdoorking online store or on ebay. It is the same part used on all of the horizontal crankshaft and vertical crankshaft 3, 3.5 and 4 hp Briggs engines made prior to 1982. Alternatively, you can fit a Magnetron electronic ignition unit from one of those same engines made from 1982 onwards, and you then just cut the wire running to the breaker points and condenser inside the flywheel. The cheapest way to proceed is to open a thread in the Outdoorking Wanted forum, asking for a coil or Magnetron ignition module for your engine. Most likely someone will reply saying they have a second-hand part available. They will then send you a Private Message regarding price, postage cost etc.
In other words this is not a big setback, but it will cost you a few dollars, especially if you want to fit a new genuine coil the same as your old one. Most of us prefer the second-hand Magnetron solution unless the engine is a collector's item. The Magnetron units have a very good reputation for reliability, and they get the whole breaker points and condenser scene out of your life. When engines such as yours get very old they sometimes wear out the tiny plunger that operates the points, in a little compartment inside the flywheel. That lets oil into the compartment, and it eventually stops the ignition unless you fit a new plunger.
