The Joystick used is a JH-D400X-R4. Make sure it is the 10K Version otherwise the output levels will be different.

For multiple reasons it makes sense to not solder the cables from the joystick directly onto the pcb but use some kind of connector instead. This assures that you can easily swap the two pins surrounding the wiper of the pots of the joystick in case your outputs are reversed.

The two connections to the gate output are swappable since they simply work as a momentary switch when the button on top of the joystick is pressed. To identify the two cables that need to be connected to the gate pads press the button of your joystick and use a multimeter to check which two cables are shorted when the button is pressed.

For the axis the wiper of the potentiometer needs to be connected to the middle pad of the 3x1 connector. If the output of the corresponding axis is reversed just swap the outer cables.