[WIRING HELP] HSH Schematic with BKPs - Coil split issue

[DiffuseReflection]

So, after getting my first pair of BKPs and discovering that my S-series is equipped with the infamous (and kinda complicated) VLX91 switch (thanks odibrom!) I decided to do the following wiring combination following the schematic below:
I'm only using a volume and another DPDT switch that is wired the same as the DPDT on the push-pull pot. With that, I just ignored the wire that goes from the 3rd lug of the volume to the tone (not sure if that's the intended way).

The problem is, that the stock QMS1 single is two conductor with a bare wire (Red, White and Bare), and no one has any info on what is what. I took the guess that the red is hot and the bare and white are ground, and wired it as follows: Red to ground at the back of the volume pot and the bare and white to the switch.

After wiring it up, I got the following:
Switch Off (Not split):
Bridge
Nothing
Nothing
Nothing
Neck
Switch On (Split On):
Split Bridge
Nothing
Split Bridge and Neck
Nothing
Split Neck

What intrigues me, is that when the split is on, I do not get any noticeable hum and when testing the pickups - tapping gently with the tip of a screwdriver - I get one coil louder than the other. Sound wise, I do get a drop in volume and a tiny sound (definitely more noticeable on the neck). My guess is that they are not split and only switching from series to parallel.

So, I'm confused and it's my first wiring endeavor (EMGs don't count as a 5-year old can install them). My guess is that the red and white/bare are inverted (the way I installed them) and something is not right with the split.

The pickups are a set of Alnico Black Hawks and the middle SC is the stock QMS1. (can definitely provide some DIs after this is all done).

 

[DiffuseReflection]

So, after some debugging I made progress and all the positions are working as intended. BUT, the individual coil split (bridge and neck) has still not convinced me that is working properly. There is no noticeable hum but drops in volume. The 3rd position without the switch active, which is the middle SC only, has little but noticeable hum (which is expected).
The only thing that is wired different from the schematic, is that the ground coming from the switch is not going to the lug of the volume pot, and instead going to the back of it (the lug is bent and soldered to the pot's back). Any input there?