I have an Atari Games optic board from '87.  I'm not sure if it came from a trackball or spinner, but since the back of the board says '87, it's a pretty good bet it didn't come out of a Centipede or Millipede.  I might guess Blasteroids, since that was circa '87.
Here's pics of the 
parts side and 
solder side.  I flipped the board about the vertical axis to take the pics, so keep that in mind if you want to compare the traces to the components.  
I followed the traces quickly, and it looks like the pins are (from left to right) on the parts side:  X1, +5V, GND, X2.  You would just have to reverse the X1 & X2 wires if the cursor moves in the opposite direction that it should when you are finished.  Hope that helps some.   
