I purchased a used Craftsman G8400 that had an issue with the engine bogging down when the PTO was engaged. The spindles and blades had rags entwined in them and I thought that was the cause of the issue. I went ahead and bought the mower. When I got home, I removed the rags and checked the spindles and pulleys and they moved freely, but the engine still bogged down. I checked the spark and found only the left cylinder firing. I bought a new Kohler coil and installed it. I rechecked the spark and found the left cylinder was still the only one firing, the new coil side was dead. I switched the coils around and now the new coil fired but the old one wasn't firing. I tinkered for about an hour and was at a loss to understand the situation.
When I bought the mower, it had a 32 584 25-S coil on the dead side and a 32 584 09-S coil on the good side. This combination of coils does not work together. I bought a new 32 584 25-S and replaced the "bad" 32 584 25-S with the new coil, and now the new coil was still not firing. I searched the forum and found this post and went out and pulled the 32 584 09-S coil out and had both coils being the same part number and that was indeed the solution.
So thanks to everyone for posting about the incompatibility of the Kohler replacement coils.