Our 2006 G35 coupe suddenly had the battery and brake light come on. We knew this meant alternator problems as it went into limp mode. We replaced the alternator, (what a fiasco) but found the plug was missing (just two bare wires) got the new plug. Even after the new alternator (and it's showing output to battery) the lights are still staying on. We've cleared all codes, retested with no codes showing. Tested output 13.5 to 14.5 vdc, but can find no reason for the battery and brake light to still show on dash. Anyone have an answer, or a place to start looking?
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The alternator circuits are pretty rudimentary, see SC 23~24 here:
https://www.nicoclub.com/service-manual ... 6%2Fsc.pdf
Are you certain the wires on F20 aren't reversed? If they are, you'll still get some field current through the LED so the alternator will charge (albeit not well) and the LED will stay lit. On the other wire, the field fuse may or may not protect the lamp driver transistor in the alternator from blowing.

Finally got a testors and plugged into the SBD Port, Alternator output is s howing 14.8 to 14.9 with the battery low. The New Pigtail to the Alternator has a Black - Red- Green wires, from the Harness is a White with a red stripe( or Pink? ) and a White with a Black stripe ( Or green ) I'm trying for find out if I have it wired correctly. I wired the. Red from the pigtail, to the White with Red( pink ) stripe, and the black to the White with Black( green ) stripe, then Green to ground. As said Voltage being read at 14.8-9 and both Brake and Battery lights stay on ( showing no codes )

No way to help you without seeing the polarizer orientation on your pigtail. It needs to match F20 in the wiring diagrams. Since F20 is shown with a single outline it means it's a terminal side view, so looking from the harness side where the wires enter the view will be reversed. White/Red goes to pin 3, Light Green/Black goes to pin 4. Hopefully you didn't reverse them, if you did then there's a good chance you blew up the lamp driver circuit in the alternator.