new to me 1976 KZ 900, wires go where?

The coil readings on the yellow red wire should be around 12.3 if the battery is 12.5.

The green and black could be 12.3 or 0.0
It just depends on where the points are in their rotation. If the point is closed for that coil, then 0.0
If the point is open for that coil then 12.3.

The battery side of the relay is good.
The starter side of the relay should be 12.5 when you push the starter button and you should hear a loud click from the relay.
It should be ghost voltage when you are not pressing the button.

The ghost voltage at the starter relay is showing that the relay is not working.
There is a break in the magnet circuit or the relay is bad. We'll check the 2 smaller wires that fire the electromagnet inside the relay.

Inside the red circle
Meter DC V
Key on
Ignition on
Engine not running

Black probe negative battery post
Red probe on black/yellow wire
What is voltage?
It will be low. It should be no higher than 0.5V
Ideally, it will be 0.0V
Hit start button
Voltage should stay around 0.0V

Move red probe to black wire.
Should be 0.0V as well
Hit start button
Voltage should go to at least 12.0V.

Schematic courtesy of Mikaw

 

good morning,
very cold in the garage this morning, 25 degrees here in Ohio.
I checked the black, yellow and black wires at the relay with key on. Both reading 52.0v. Something isn't right since those readings aren't even close to what you were expecting.
I am going to let the garage warm up a bit and then recheck all the other readings.
@F64

Is it possible that the meter is on the wrong setting, and what you are actually measuring is 5.2v rather than 52.0v? If the setting is correct, I would be looking for another meter to borrow in order the validate the accuracy of your meter. If you do not have a friend who will loan you one, perhaps a local auto parts store has one for loan or rent.

ok, well I just bought this one and using the setting you see in the picture attached.

 

To measure the correct DC voltage you have to use the black connecting terminal for ground/negative.

 

ok, I'm an idiot!!!  I will take all new readings!!

Ok, latest test - key on, ignition set to run(appears in my previous tests, the test wires were in the incorrect ports and the ignition was not on run) . OK Black probe on negative battery terminal, Red probe on starter relay red side = 12.2v. When I move the red probe to black side of starter relay it reads 2.7v, when I press starter button I hear a click and neutral light goes out, volts go to 12.2 v. 
Left coil red/yellow 12.5 , green black .3v
Right coil y/red jumping around from 50v to 130, green black . 3v


 

You're getting lots of good advice here and I don't want to confuse things, but I wanted to add the following thoughts.

Kawasaki did a pretty good job of organizing their wiring back in the day.  Most wires terminate in plugs and most plugs only require common sense to attach to the main harness.  ie: look for the same number of pins in both ends of a plug and match them up.   If someone has butchered the plugs you can always rely on connecting a coloured wire to the same coloured wire somewhere nearby.  The schematic shows every colour and also shows the pin type (male vs female and also single vs double) you should expect at the terminal where no plug exists.  Lastly, if the harness is still in reasonable shape you can expect that wires coming out of it at various locations will have a device nearby to connect to.  This applies to things like the rear brake sensor, or the horn, etc.

I am currently rewiring a 650 with a badly butchered harness, and the above general guides have enabled me to rebuild the harness and reattach everything.  I hope the above advice is helpful.

Next - Inside the red circle, Meter DC V, Key on, Ignition on, Engine not running @F64
Black probe negative battery post
Red probe on black/yellow wire
What is voltage?  12.49. The neutral light is no longer on, seems after the click it has gone out.
It will be low. It should be no higher than 0.5V
Ideally, it will be 0.0V
Hit start button
Voltage should stay around 0.0V

Moving red probe to black wire.
Should be 0.0V as well , black wire is also 12.49.
Hit start button, nothing happens when pressing start. volts remain 12.49
Voltage should go to at least 12.0V.

Let's look at the starter relay first.
A couple of things seem off.

Oh, when your meter says MV in the top right corner... It's milivolts not volts. So the decimal point will move 3 places to the left for volts.

It seems your starter button may be stuck.
When you press the starter button it sends 12v along the black wire to the relay.
When the button is not pushed, the voltage on that black wire will be 0.0volts, but your wire reads 12v without pushing the button.

You may have 2 issues.
The button is stuck and your ground wire to the relay is not connected.

Gotta run.. Will add more in a bit
Your right coil is also has ghost voltage.
The yellow/red seems broken for that coil

Thanks for the help @F64 and all the other replies. Very helpful.I am attaching a photo of the starter relay and it appears black ground wire is connected to it and wraps back behind the relay to another gizmo. A few wires running into that.I am also attaching a photo of a loose wire (has the electrical tape on it) below the relay that is black and doesn't appear to be a plug anywhere near for it.  

another question, does anyone know if the throttle control and starter button can be taken apart to check the spring and clean the contacts? I could give that a whirl before buying one.
Thanks