Can you guys confirm that my Fender Modern Player Telecaster Plus 3-wire humbucker is wired in parallel mode?

The humbucker has 3 wires, a red, white and green wire + shield. The green wire and shield are grounded to the tone pot.
The coil split switch is a 2-position DPDT on/on toggle which gives you either dual coil or split single coil. The humbucker red wire and the red out wire to the 5-way switch (coming in from left in picture) are both soldered to the lower right switch terminal. This means the humbucker's red wire is always connected to the 5-way switch.
The humbucker white wire is soldered to the coil split switch's right mid terminal. This means the white wire is either connected to the humbucker's red wire or completely disconnected.
There is no black wire coming from the humbucker.
Is it possible to wire this 3 wire humbucker with a 3-way toggle for series/split/parallel?
My best guess is: The red wire is the inner (slug) coil out which is always hot. The white wire is the outer (screw) coil output. The green wire is the ground for both coils. If this is true then the humbucker is wired from the factory in parallel when the humbucker's red and white wires are connected (red and white are hot outs from the two coils) and split when you flip the switch and the white wire is not connected to anything.
It looks to me like this 3-wire humbucker is not compatible with a series/split/parallel switch because there's no way to get the serial mode. Sound right?
I have already swapped out this pickup for a SD Invader and replaced the split switch with a series/split/parallel. I ask this question because other guys with this guitar are contemplating swapping the split switch out for a s/s/p.
Thanks in advance,
Rob

The humbucker has 3 wires, a red, white and green wire + shield. The green wire and shield are grounded to the tone pot.
The coil split switch is a 2-position DPDT on/on toggle which gives you either dual coil or split single coil. The humbucker red wire and the red out wire to the 5-way switch (coming in from left in picture) are both soldered to the lower right switch terminal. This means the humbucker's red wire is always connected to the 5-way switch.
The humbucker white wire is soldered to the coil split switch's right mid terminal. This means the white wire is either connected to the humbucker's red wire or completely disconnected.
There is no black wire coming from the humbucker.
Is it possible to wire this 3 wire humbucker with a 3-way toggle for series/split/parallel?
My best guess is: The red wire is the inner (slug) coil out which is always hot. The white wire is the outer (screw) coil output. The green wire is the ground for both coils. If this is true then the humbucker is wired from the factory in parallel when the humbucker's red and white wires are connected (red and white are hot outs from the two coils) and split when you flip the switch and the white wire is not connected to anything.
It looks to me like this 3-wire humbucker is not compatible with a series/split/parallel switch because there's no way to get the serial mode. Sound right?
I have already swapped out this pickup for a SD Invader and replaced the split switch with a series/split/parallel. I ask this question because other guys with this guitar are contemplating swapping the split switch out for a s/s/p.
Thanks in advance,
Rob
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