Fender Jazz Bass Special 1985 (Japan) Hardware

I would look at the Hipshot HB2 with a d-tuner for the E string.

 

If you replace the tuners, you might have a bunch of exposed holes from the tuners that are on there now. Don't know much about your bass, but Japanese tuner base plates are usually smaller and have different screw holes.

 

If none of the following fit, Schallers might but I doubt it; as good as they are, many overlook Schallers.
Here is the site for Gotoh, they have several different machines it could be so I didn't copy the spec sheets, You can click on any tuner and the spec drawing is down the page.
Here is dimensions for Wilkinsons

 

Yeah, the Hipshots are a bit spendy, but are very nice - I bought some of the Wilkinsons off ebay, and they were so crappy I decided not to use them and bought the Hipshots anyways... Here's some pics of them on my JBS:





The Hipshots were a direct fit, and have worked out great - I purposely bought the lollipops because that's what I wanted... If you browse ebay a bit, you can find some deals on the regular tuners for your bass...

 

They appeared to be, but the Wilkinsons were so crappy I refused to put them on my bass - I hope yours are more to your liking, because mine were a total waste of money...

 

Cool bass! If those don't work out, post pics with one of the tuners removed. It would be much easier to make recommendations if the holes are exposed. That way we can tell if the second set of tuners involved mods or not.

 

Beautiful bass! I own/play one that is similar but had the gold hardware. Be sure to post pics when she's all done.

 

I recently put Wilkinson's on my Squier VM Pbass- they seem very nice, although a little stiff on turning, but worth the price I paid for them.