The kill wire runs up under the engine's blower housing.
"Kohler".
"usually" on those, if you lose spark because of defective wiring or switch or whatever, it'll lose spark on BOTH. The kill wire is connected in series to both modules (aka coils).
Now with that said, if you're losing one cylinder (which I suspect you are), pull the blower housing off and see what kind of coils you have. If you have the 3 or 4 wire kind (which are DSAI coils), replace both of them with the new MDI kit, available from Kohler (part # 32 707 01-S) and I think also Kubota under a different part number of which I do not have handy. Kubota may be less expensive so double check.. DSAI coils have/had a very high failure rate. If you have the single wire version, disconnect both kill wires, then start the engine. If it runs on both cylinders again, your coils are good and there is a wiring issue (grounded/shorted) somewhere.
if you have spark on both cylinders and it's using a ton of gas/low on power, check the throttle cable adjustment and make sure it's not choking. Also if ya ain't already, check the air filter make sure it ain't plugged up.