Small Engine Troubleshooting Problems? Ask a Mechanic Now.
Kohler twin engine? Does the engine have oil guard system, that would kill spark if oil pressure drops? Oil sender may be killing spark.? What is the full engine model number?
You are giving me the mower model. Looking at it , it shows an ignition module for each cylinder as having two wires to each coil.
If the ignition modules have two wires, the engine has a spark advance module. Yellow wire to modules is the trigger wire from the spark advance. Locate the spark advance module and remove the white wire, If stil no spark replace the spark advance module. I'm looking at an SV700 series service manual.
Manual page 35. Link above.