Most ball mice have dual sensors in each wheel (2 sensors in one chip). 2 sensors X 2 chips = 4 sensors.
This is how it detects direction (see PL1's post above).
Im not 100% sure, but it looks like they used two single sensors to accomplish the same feat as one dual sensor would do.
If this is true, you will need to wire to each sensor, with the wire connected to both probably being +5vdc.
If I am right, it will be simple. Just treat the two sensors (also know as receivers), as 1 dual sensor.
Remove both sensors, tie your trackball wires to one leg of each sensor (don't use the legs that are connected together, unless it needs to connect to the trackball, I cant remember, need to look it up.)
I know there is one or two chips that will not work as a trackball hack because they look for the receivers switching the ground instead of +5volts. (I think. This was discussed in a post a few years ago, I will see if I can find it.)
Edit: My posted link refreshed my old mind. The chip that will not work is looking for the receivers switching ground and positive to the chip. I guess the chip uses the serial pulses (positive or negative) the same as a trackball (and most mice) use 2 positive pulses.
Follow the traces on your circuit board. It looks to me like one leg of each sensor goes back to the chip. The other leg of each sensor are tied together and most likely to +. (See if there is a capacitor wired to this trace, it will probably be the + side of the cap wired to the trace.)
If you have a DVMM, power up the board and see if you have +5VDC to ground on this bus. (Ground is probably the thick trace wrapping around the outside edge of the board.)