If it is in fact a digital switch, you wont be able to use it, as is will not close circuit on 2 wires when moved to a direction like a regular switch. In other words, if you would probe with a multimeter to see which wires are shorting when you move the joystick to a direction, none will do it.I see, you don't think that small joystick would carry the current to trip a relay? I may need to look at the electrical schematic from my truck.
I have a larger joystick, but would really like to explore something thumb-sized. I'll keep thinking on it.
Mike
(Digital switches will have some electronic on them)
However, if the joystick switch is analog, then you could use one.
Good luck with your project
Cheers
Dan