This manual might be of help.
http://www.mymowerparts.com/pdf/Koh...al-K91-K141-K161-K181-K241-K301-K321-K341.pdf
http://www.mymowerparts.com/pdf/Koh...al-K91-K141-K161-K181-K241-K301-K321-K341.pdf
If you are ambitious you could remove the harness, lay it on a big surface and copy a new harness. This can be a major PIA and would require correct gauge wires in place and a knack for soldering or crimping. If (the machine is worth it) you are pressed for time I would see if you can buy a new harness. Restoring a burned harness with electrical tape can be tedious and the tape may not provide enough insulation resistance. Also some of the wire may have been embrittled which may snap under vibration. Patience and good luck.