JC - I didn't respond to your email but will respond here. If you need fast help, go to my forum on my web site where I look in, even on the weekends, to answer questions. I don't have time to respond to individual private emails anymore.
In any case, first, pull the bulb out of your new turn signal. Look at the base of the bulb holder. There will be either ONE little contact or TWO contacts. The single contact is a turn signal that ONLY works as a turn signal and the double contact means it is not only a turn signal but a running light.
If you have ONE contact, and have two wires coming off the turn signal, one is a hot and the other a ground. If you have TWO contacts, both wires are hot and you must ground the turn signal.
On almost all KZs, Kaw uses a black/yellow wire with a metal ring that goes between the turn signal and nut that holds it on to provide grounding. If your turn signals doesn't have a metal body and there is no metal contacting the metal ring on the end of the black/yellow wire, you will have to take a screw out of the bulb holder and attach a piece of wire to join to the black yellow wire. This is your ground.
As far as the hot wire(s), Kaw uses pretty much the same wiring colors. Too bad you didn't mention the colors of the wires you suspect. Generally, they will go with light gray and medium green for the turn signals. One color is used for one side and the other for the other side. Check your rear turn signals to figure out which color goes to which side. I can't remember but if you do hook them backwards, it is just a matter of swapping the plugs inside the headlight shell.
Since you have what appear to be TWO hot wires in additiion to the ground for each side, you may have front running lights. There is no standard color I know of but some Kaws use blue for the front running lights.
If you HAVE A TWO CONTACT bulb holder, I think the bulb will only go in one way. That means that there will be a long/large filament and a small/short filament touching the contacts and the small filament is the running light... the larger/longer will be the turn signal.
Since you have different types of turn signals, with different bulbs, you will also need a HEAVY DUTY turn signal relay. They sell them at an autoparts store. Your relay has |_ shaped prongs. The ones at the autoparts stores have prongs shaped like this and will be cylinder shaped about 1 inch long. A heavy duty flasher relay should cost about $7.