Your engine was manufactured in 1978, and Briggs did not fit the Magnetron electronic ignition until 1982, so it has breaker points, and that is where the wire that runs under the flywheel goes.
The first thing you need to do is test the coil, then ground it properly and set the flywheel to coil yoke clearance properly, and see if you then have spark. If you don't, there are various ways to proceed from that point. To restore the engine, you would begin by removing the flywheel and taking the tin cover off the compartment which has the points and condenser inside. You might find the points have closed up, or just possibly the compartment is swimming in engine oil. If you do, you will know what is wrong, and would have to choose between keeping it original, or fixing it permanently and easily by fitting a second-hand Magnetron (a simply bolt-on replacement for your original coil). Keeping it original would involve resetting the points if there is little or no oil in the compartment, and seeing if it then has spark. If it doesn't, you'd need to consider a new condenser. If the compartment is full of oil you could begin by replacing the plastic plunger which operates the points, but if it is still leaky with a new plunger you'd have to ream and bush the crankcase where the plunger passes through it: a costly process because of the need to buy a reamer and bush.
So, you have a choice: post a request for a Magnetron on the Wanted forum (giving your model number of course) or remove the flywheel and find out what is going on.
