Small Engine Troubleshooting Problems? Ask a Mechanic Now.
Welcome to JUST ANSWER small engines, let me try to help you !! I don't know it all, but maybe together we can get you a satisfactory answer!
Twin cylinder engine. Run a cylinder test, loosen the spark plug wires, and with engine idling, remove one wire at a time, if engine dies when one wire is removed, the opposite cylinder is not firing. It may have no spark, from a bad coil. Or it can have the rocker arm problem again. Kohler has had engines with rocker arm problems and they replaced the cylinder head to newer style setup on he rockers. But that may not be problem now. More common is a bad coil. And Kohler wants you to replace both coils at same time.