I'm sharing this here in the interest of having the pinout in question documented on the net, in hopes of the process or pinout being useful to someone.
I wanted to connect mice to my GA586-TX2, but there was no PS/2 bracket with the board, I could not get serial mice to work (ctmouse or the M$ driver would not detect anything), and the manual contained no pinout for the header.

The pinout was determined by probing with a multimeter to find the +5V and GND lines. With J2 pin 2 connected to the 'meter's COM probe, the other 3 pins read 5 volts, but with pin 1 connected to COM, pin 2 read -5V (as expected with inverse polarity) and pins 3 and 4 showed negligible readings. This indicated that the first 2 pins were involved in power delivery, and not pins 3 and 4. After that, it was a matter of trial and error to determine the Clock and Data pins, and the header was reverse engineered. Nothing groundbreaking, but hopefully this will help someone or save their time.

Good regards