Small Engine Troubleshooting Problems? Ask a Mechanic Now.
Twin engine Kawasaki. If both cylinders are firing and the spark is weak, the only common part is the ignition module. I would run a cylinder test, loosen the spark plug wires, and with engine idling, remove one wire at a time, engine should continue to run. If it dies when one wire is removed, the opposite cylinder is not firing. If one is not firing, likely a bad coil on that cylinder. If both cylinders are firing, I think you need the ignition module.
Weak spark on both cylinders. Replace the ignition module.
# ***** in the parts diagram above. PArt number AM132577
Let me look for a troubleshooting diagram for it, it runs over $300!
Here , this may help.
I see question is still open, did you get to check the igniter?