OK. I've had to admit defeat on finding the amended wiring diagram. Maybe I dreamed the whole thing up. Gotta lay off the ether :-/
However, what I have got is the wiring diagram for EK ute/van, which appears to be what we need, since the set-up for the rear lights is the same as FCs fitted with amber turn signals.
I've put a copy of it
here, since I've had to scan it at a size too big to display here. Right-click on it and you should be able to d/l it to your machine.
From my (admittedly cursory) examination of it, it looks like the white wire was used in the previous (flashing brake light) version to run power through the brake pedal switch for the indicator's operation. In the later version, it looks like it powers the reversing light switch?
If that's right, it's unrelated to your indicator problem, which in both versions shows a black wire from the flasher unit up to the tell-tale.
Hope this is some help, and sorry it took so long.
cheers
RET