I saw this question last week and it's been bugging me. But I haven't been near a computer since then (only my phone, which sucks for editing).
I modify stepper motors from uni-polar to bi-polar on a regular basis.
Because you don't have terminal numbers on your coil connections, I'm going to number them according to their position of the numbers on a clock face. Bottom pair of wires comes from the notch at 7:00, next pair of wires comes from notch at 8:00, next pair of wires comes from notch at 10:00, last pair of wires comes from notch at 11:00.
My preference when changing a stepper motor from uni-polar to bi-polar is to wire the coils in parallel if possible. This reduces the inductance (as opposed to a series connection) and also reduces the resistance. The reduced inductance allows faster step speed and the reduced resistance allows higher current operation.
I strongly suspect that each pair of coils is bifilar-wound with 2 different colored wires: tan & red. That is: both wires are wound at the same time. To make the stepper uni-polar, the tan wire from one end is connected to the red wire of the other end and connected to the common point.
I think that one end of phase A is the pair of wires coming from 7:00 and the other end of phase A is the pair of wires coming from 10:00
That would make phase B the pairs of wires coming from 8:00 & 11:00.
The quick way to find out is to gently un-solder the coil wires connecting to the common traces (brown wire) and ensure that all coil wires are now not connecting to each other. A simple continuity test will confirm which wires belong with each other (4 coils, 2 wires each).
If in fact the coil wires are as I suspect, the easiest way to convert this motor to bi-polar is to connect both wires belonging to a phase to the same solder pad going to the Yellow / Blue wires (phase A) and White / Red (phase B).
There wouldn't be any wires going to the common traces on the PCB (Brown wire).