In your hand, you're holding the 3 wires from the "Regulator" side of the combination Reg/Rec. They plug into the stock 3-prong plastic connector, color-to-color. The new unit you have pictured is a Ricks Motorsport, model 10-100 and it works fine for your 550.
Just above your hand in the background is the stator harness plug carrying the yellows, red and green from the "harness side" of your bike, and you have the plastic plug from the Rick's correctly plugged into the "Rectifier side" of the device.
This is the starter solenoid. Either of those connectors can attach to either post. One comes from the battery POS and the other goes to the starter motor.
Those wires are on the harness side, the Yellow/Red stripe is from your electric Start button. It connects to the female connector in your next picture, which should in turn connect to the starter solenoid. The Brown/White female is a double connector that comes from the fuse block, and provides switched power from the key to the front of the bike for your tach and speedo backlights.
These are the 2 wires that plug into your starter solenoid. The Y/R we discussed above, the Green/Red is the NEG side of the solenoid relay, Y/R being the POS side.
Thank you. Thank you. Thank. You.
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