Hi all - the extra wire is not related to phasing at all.
The third thinner black wire is a ground wire attached to shielding foil underneath the polepieces, primarily for use with certain buffer preamps (i.e. audere) that require grounds to be separated (my SV came with a small note detailing this, which said most of the time, such as passive, just sodler it to the same location as the thicker ground wire)
I believe this is a recent change and it would appear you neck pickup is older than the bridge.
For further clarification, email Nordstrand - they are VERY responsive to emails (say hi to Stu).
Jamie