With the deadman's switch ACTIVATED (IE in running mode), there should be OPEN CIRCUIT to chassis. Grounding the small terminal on the coil stops the engine.
If you have no spark, the coil has failed - not uncommon at all. New coils are available - at a price. A better - and longer-lived alternative - is to fit a Tecumseh coil. These just need one extra mounting hole drilling, and the other enlarging. (Relatively) easy to get, and not too expensive. Will almost certainly out-last the rest of the engine. I've done about 20 and never had a repeat failure. Most of those coils were used before I fitted them.
phil_saunders(a)bigfoot.com
Phil Saunders, June 2012