Click link and save a copy of the service manual to your computer.
The manual gives good instructions for troubleshooting ignition problems.
Be prepared to trace some wiring and/or find some safety switches on the tractor.
All kill wires, whether from the key switch, or one of the safety interlock switches, ultimately feed to a single "kill wire" circuit which connects to the "kill terminal" on the ignition magneto. Disconnecting the kill wire from the kill terminal will determine if something in the tractor wiring is keeping the coil "killed" or if the coil is defective.
If the spark returns after you UNPLUG the kill wire from the kill terminal of the coil, the coil is good and your problem lies in the wiring or one of the interlock switches.
Note this: Mice have been known to chew wire insulation to the point that a kill wire touches metal and if the kill wire grounds out, the coil is in killed mode.
DO NOT attempt to test anything in the kill circuit by applying 12 volts to anything. It will be the death of the coil if you do. The magneto ignition on this Kohler is self energized by the flywheel magnets (hence the name "magneto") and requires no outside input to make a spark.

Here is a link that might be useful: Kohler manual

I've been reading the manual for some testing, the coil seems to test as good. I got 15,000 ohms across the coil and thats in the high range. I'd go out and test the coil installed on the tractor with the kill wire unattached but the mosquitoes would eat me up. So I'll try it in the morning, thanks...Dave

***"I got 15,000 ohms across the coil."***
Yep, that looks just like the picture in the manual to me.
Don't feed the mosquitoes.