First off make sure its the magneto not just a kill switch or wiring.
I hate to see people load up a parts cannon and blast away installing "NEW" parts that are defective right out of the box.
Its not a difficult job to remove the engine on them to get to the flywheel shroud.
I 100% guarantee you will find the coil packed solidly with Debris and the cooling fins,and the stator under the flywheel.
Most times it is the killing factor of these ign magnetos and engines.
While the engine is out, one can address any oil leaks, also blow out under the flywheel.
Also you can check the rag joints/driveshaft conditions as after 40 years they do need some attention unlike todays mowers that require no militance, because in 7-10 years you just sell them to scrap to be recycled.