Fender Japan does make a 7/8 Jazz Bass called the JB62M, but they've only introduced it fairly recently (within the last 5 years) and there is definitely no lefty version. They did a medium scale Precision once in the mid 80s (32" scale, slightly downsized body) in both righty and lefty versions, but as far as I know a similar Jazz Bass was never offered as a lefty. So I have to agree with Stingray5
. I also agree the controls and the sidemounted jack aren't original.
That black medium scale E-series Jazz is a really cool find! I've never seen one before or heard of it.
Here's one of the new JB62M's next to its bigger brother, the full-scale JB62US. I'd be all over that if they did a lefty run!