Glad you’re enjoying the game!
I’m not familiar with that joystick, but there weren’t a lot of them that worked with the C64 second button.
You can also trigger the same function by plugging a second joystick into port 1 and pressing fire.
Ah - so it's a second joystick that is used for the game. Now I understand - thank you. Further research has indicated that the second fire button on the Epyx/Konix 500XJ only works with a Sega Mega Drive and the NES. So not the C64 sadly :(