Are you asking about the yellow wire in the home-built harness?
I would disagree with that because an "auxiliary" connection to the battery should not need a bolt & nut -- it should slip under the main battery connection but it does appear to be a nut & bolt from a battery connection. (That yellow wire is way too flimsy to substitute.)
That supports your guess -- if the green thing is a fuse. Only looks like maybe a fuse to me. Need to see more. I don't have any idea why a fuse would be mounted there.
On my bike, the red & red+white wires are the power connection to the stock r/r. There's no telling what's going on with a home-built rig installed. My bike still starts with that connector empty now that I've got my Shindengen r/r direct-wired to the battery.
You can say that again!
Step 1: Verify that the new battery is charged and putting out between 11.5 and 13.2 volts.
Step 2: Verify that you've got the battery connected properly -- all connections clean and tight.
Step 3: Check your fuses, particularly the main 30 amp fuse. (Mine is NOT located in the fuse box. It's under the seat.)
Step 4: Follow the main positive cable from the battery to the starter relay and make sure everything is kosher.
That's as far as I can take it because I don't know specifics of your bike. If it was mine, I'd be checking the Gonzo harness connections and the start switch next.