The joined white and red wires are the 'series link' between the two coils. One of the coils will be reverse wound, reverse polarity to the other coil so linking them together gives you a hum cancelling/bucking pair... hence, humbucker. When you split the coils and combine it with a single coil pickup you want the split coil to be the reverse wound reverse polarity of the single coil pup thus giving you a hum cancelling pair. On a strat the middle pup is RWRP compared to the bridge and neck so in positions 2 & 4 on the lever switch you get a hum cancelling pair with bridge & middle and middle & neck, respectively. This is what you want to achieve when you split the hot stack, if you get what I mean.

Btw, you don't need to separate the red and white for testing. So, green->hot and red & white->ground for the first coil, then red & white->hot and black->ground for the other coil. It should be very evident which coil cancels the hum with the neck single coil.