Approach it backwards? Ask Kohler which Mfg. typically uses these engines, then try to download a manual showing a wiring diagram. e.g. On Craftsman there's a wiring diagram with color codes for wires going into connectors on the engine side and the "tractor side."

Probably easier to get a "four pin" connector and remove the engine connector and install the new one. Worst case, put in a terminal block. Easy enough to follow the wiring to determine what goes where. e.g. If a red wire leaves the regulator, it's not going to change color in the wiring harness, etc. Make sure you incorporate a fuse in the one I just mentioned, that's always supplied by the tractor, etc. Mfg.

Also, if you are successful getting a matching connector with wiring harness, it'll probably be too long or short and you'll end up doing "surgery" anyway.

Good luck,

Ev