Kohler has a nice website that has manuals for each of its engines. I would start there and see if I could identify the part number.

Next I would contact my John Deere dealer. (Not a big box store). They usually stock or have access to all of the parts to keep their equipment running.

How many & what color wires?

There's a good chance that if it plugs into the Deere harness, it may be a Deere part.
You really didn't say what it was, just what it wasn't.

Kohler will service the connector and terminals- but you really should have the spec # as well. Post back if you have issue. Below is the link, use internet explorer and enter as guest.

Here is a link that might be useful: kohler

Hey Guys, thanks for your help. I checked JDPARTS and I think I located the plastic connector. It's "M133018 connector". I see I can order this from a vendor. So now the question is, the connector has very small female bullet connectors inside. Can anyone tell me what size/kind these are? Thanks for your help. - Jim