I can tell you what the Briggs wires are.. I just installed 21 HP Intek
Four wires total..
You have two power wires, red and a orange jumper both come out of square block (regulator) You may have a true two wire unit..
The one with the small inline fuse looking wire is you DC and goes to battery / charging system.. The other is AC and goes to lights.. If lights are worked by key switch it most times runs to switch..
Mine just has a jumper and both wires are DC split into two wires from one..
A gray wire (I think) going to bottom of carburetor bowel connected to the fuel shut off valve..
This wire needs power when key is turned on to make tiny solenoid open and allow gas to carburetor.
The black wire is the magneto kill wire that connects to ground and kills the spark to plugs when key is turned off..
Make sure you do not send power to Magneto kill Wire because it can do damage I read..
You can maybe figure out the Kawasaki but just looking at mower and engine..
If you have a multi meter you can maybe check what wire is what if your handy with wiring..