You can't activate the Axis UI from external physical controls. This isn't a disadvantage, as it means that the hardware controls are handled entirely in the realtime layer without passing through the less-reliable GUI layer.
The AXIS GUI exports HAL pins that report the currently selected jogging axis and increment. You can choose to use these pins or not, as the mood takes you.
I see you have a jog-wheel _and_ a joystick. Is the joystick a switch or proportional?
You need to connect the jog-wheel to a quadrature counter to convert clicks to a number in HAL. To advise on how to do that we need to know what interface hardware you are using.
There is an example here of connecting a jog-wheel using the parallel port
linuxcnc.org/docs/html/examples/mpg.html
You will see that it uses parallel port inputs to select the active axis, which would be connected to a elector switch:
To select axes from the GUI rather than a switch you would change
net mpg-x axis.0.jog-enable <= parport.1.pin-04-in
net mpg-y axis.1.jog-enable <= parport.1.pin-05-in
net mpg-z axis.2.jog-enable <= parport.1.pin-06-in
to
net mpg-x axis.0.jog-enable <= axisui.jog.x
net mpg-y axis.1.jog-enable <= axisui.jog.y
net mpg-z axis.2.jog-enable <= axisui.jog.z
