I recently bought two "Tiny Trackballs" from Electronic Goldmine. These are little surplus trackballs made some time ago by Alps and come with no hookup info. Google didn't helped: no info about this board or its controller (a SMD 24 pin IC marked ALPS / 3JA1DT002 / TB6012CF), so I had to derive myself the schematic (from the PCB) and guess how to hookup this the connector pinout and the protocol used. These are the results of my experiments and not official data, so there may be errors, use these info at your own risk. And also, my english is "as is", comes with no warranties, may be broken :-))

Connector / solder pad pinout (see images below):

1 - Vcc (3.3 ... 5V ?): The minimum voltage for operation is around 3V, and the 10uF capacitor is 6.3V rated, so I suppose the circuit was designed to work at 3.3 or 5V or both)
2 - Optional reset input: Active high, has internal pulldown (70-80 kOhm). When reset, the serial output send one byte ("M" character, as the standard mouse reset sequence, see link below)
3 - Serial output: TTL level, 1200 bps, 7N2 or 8N1 (standard 3 bytes Microsoft 2-button serial mouse protocol, for more info see here: http://www.hut.fi/~then/mytexts/mouse.html)
4 - ??? - This pin is connected to pin 19 of the controller IC, but it floats (no pullup/pulldown or any sign of activity) and seems to have no function
5 - Optional external right button input: active low, has internal pullup (70-80 kOhm)
6 - Optional external left button input: active low, has internal pullup (70-80 kOhm)
7 - GND
8 - NC (not connected to any other component)

So, if you want to monitor ball movements only and do not need buttons or external reset, the minimal interface require only three wires: Vcc, serial out, GND.
I tested the trackball at 5V and 3.3V, and both seemed OK for proper operation.

Measured operating current:
Icc @ 3.3V : 5.6 mA - When the device is idle for more than 3-4 second (no serial output) Icc drops to 1.0 mA
Icc @ 5V : 7.3 mA - When the device is idle for more than 3-4 second (no serial output) Icc drops to 1.9 mA

I don't know what's the function of pin 4. I have tried pulling it down/up/or left unconnected and noticed no change in the operation of the trackball, nor any signal/pulse coming from it.
 

An alternative to connecting the board with a 1mm-pitch flat cable connector, is soldering tiny wires on the rear of the board: there are 8 useful small copper pads (probably designed for automated tests).

I tested this interface on a PC running Linux. The output level of the interface isn't true RS232, only positive levels, but it works. Your mileage may vary :-)

Linux settings (for COM1 port)

gpm (text console):
gpm -m /dev/ttyS0 -t bare

XFree86:
Option "Protocol" "Microsoft"
Option "Device" "/dev/ttyS0"