Welcome.
Generally the JS II was a "short scale" bass with a nominal scale length of 30.5". Usually strings that give a suggested scale length in that vicinity or say "short scale" should work. There are sets aimed at Hofners that say "short scale" that really are too short but otherwise 'short scale" is usually safe. I can read string packages later today and see if I have anything to add.
Roughly speaking the JS was in production from 1970-1977 with the specs on the very early and very late models being "unusual". Circa 1973 or 74 a long scale JS was introduced. That is a 34" scale. If you count frets, the long scale had fewer. My memory says 21 for the short scale and 19 for the long scale but I could be off. If you have an eye for detail and have seen a lot of short scale JS basses, the bridge position looks "off" on a long scale.
I looked at the scale guide for Rotosound
here. If I had to buy something for my JS right now, without measuring anything, I would go for what they call medium scale since they say 30.5-32" and I think their short scale may be for the Hofners alluded to above. Perhaps that is your solution?