This is a resistive analog joystick, very similar to those found on the PSP1000. These compact joysticks are different in that they have a very interesting 'slide' feeling.
From our customer regarding pinouts:
With the nub up and facing you, and the pins on the bottom away from you and pointing towards your chest, from left (pin 1) to right (pin 4):
1) x-axis output
3) y-axis output
Just to make sure I'm clear, my pin 4 is the one closest to the two screw/mounting holes. When connected to an Arduino, I get a range of about 128 to 775 on each axis, with enough consistency to check if it's at -x, center-x, +x, and -y, center-y, and +y.
The cap is removable, and is covered with a 'sticky' material so your thumb won't slide off.
The pads are spaced by 2mm.