Umm - not sure. 
Processing is running on a PC and the relay is (currently) on the custom joystick board. Immediately I can’t think how the PC/Processing would trigger the relay without yet another com port.
Originally when I was a Logitech joystick, the fire button pressed was just sent to two existing contracts on the joystick (previous buttons). I wonder if I overlooked the issue of the possible false triggers plus now the extended delay has been added.
It seems the joystick is (as expected) pretty much an open-loop affair when accessed as an HID controller. I did try serial but even at high baud rate the delays were so slow that the cursors were drawn in a very clunky manner.