No, with BKP colours, with a reverse-magnet neck pickup installed the conventional way round, it would be Green & White for the coil split, Black to hot and Red (plus Bare) to ground.
Then in the split positions you should always have opposite-polarity coils active, so it'll be hum-cancelling.
If that doesn't work (I'm never 100% sure!) then swap round Red and Black.
(If you do use a normal pickup (non reverse polarity) with the screw coil facing the bridge, then it's Red to hot, Black to ground - again swap if it doesn't work. But Green & White will always be the coil split.)