So after doing a little research am I right in thinking that I need a 4 PIN Rectifier?
2 Yellow from the stator to the rectifier... one ground from the rectifier and the other to the battery (with fuse in circuit)?
Millhouse, what do you want to do?
You're kinda livin' off the grid with your lash-up!
Electrically, you can rectify the single-phase AC output from your alternator power winding; however . . . Kawasaki, in its wisdom, combined a VOLTAGE REGULATOR with their OEM configuration.
The alternator is DUMB; it just puts out alternating current, dependent upon how fast its rotor rotates. Without regulation of that voltage, some undesirable consequences may occur.
Looks like a used KLR600, or perhaps even a KLR250 rectifier/regulator would insure safe, reliable DC current.
I don't know if you're trying to assimilate components from an electrical supply store to provide battery power or what. With some circuitry knowledge and a feel for the current and voltage magnitudes, that can be done. However, plugging in a purpose-built rectifier/regulator pre-solves all the circuitry problems.