Have you checked it against the wiring for an Ikari LS-30?
According to the manual that I found at crazykong.com, this joystick is SNK part number LS-40. Surprisingly the manual doesn't give the pinouts though.
Hmm, the manual calls it "LS40 - 24", and the "standard" old-school optical rotary was called "loop 24". I'm guessing these two are the same?
If that's the original wiring harness, Red and black should be 5V and Ground respectively leaving the other two to be the signal and clock wires. That makes sense as that would match the pinouts for the optical boards on Happ, Atari, and Wico trackballs.
Technical Note: The "other two" wires in happ, atari & wico TB are not signal & clock, but x1 & x2 (or x & x'). There are two optical sensors per axis (often both in one case, though); one wire is the
raw data from the first sensor, the other wire is the second. I don't have the loop-24 stick, but happs optical rotary is like the TBs.
If it was actually "signal & clock" wires, which usually means direction & speed in optical sensors like these, extra processing would need to be done on the sensor board. Which is why it was rarely done in arcade hardware.
Minor point, but the difference is why the mouse hacks are possible in all but a few sensor boards.