Yes you were right about SN had them typed wrongModel number are wrong so they need verifying.
But the first looks to be 313707-0126-E1 (2002) and the second looks to be 31A707-0525-B1 (2008)
Both six pin harnesses appear to be the same.
And I hate it when hacks up a wiring harness. That why I have the Molex connector housings with pins and sockets to correct the hacks. The connectors with pins and sockets are AMP versions.
The older Walbro carburetor came both without and with solenoid. If the solenoid is not present just the solenoid connector disconnected. Don't close that circuit as it would be a dead short circuit.