That is the alarm connector and no that wire is the immobilizer, gray with red trace. There is 12 volts there if you want to charge your phone between races and some other neat stuff...
check that, brown /blue wire ... and I was able to recreate exactly what you described with the "gear" flashing, I slowly pulled the shifter up from neutral to 2nd with engine not running and presto...
So RC_guy might want to check wiring connections, I just checked to be sure 3rd gear is a yellow wire no tracer...