Judy,
It's definitely a Japanese made machine. The
J-A 4 is the typical type of marking the Japanese industry puts on their machines. According to a chart I got from the Yahoo Japanese machines group it was possibly made by Maruzen/Jaguar. That company is the same one that made the 158- series Kenmores for Sears. Very good machines.
You might check for the bobbin cover / slide plate from Sew-Classics {
http://www.shop.sew-classic.com/ }, at least it's a good place to start looking.
If that machine runs and sews, I would suggest restraining your BF from taking it apart. Removing the inspection plates on the top and rear and opening the face plate for a good cleaning and oiling is all it should need. They are not rocket science inside, but they are not as simple as they'd seem and can be knocked out of adjustment if you turn the wrong screws.
The bottom needs a good cleaning, but nothing intrusive. Just some good brushing down with oil or kerosene to remove the old varnished oil. That's the amber colored gunk on the all the parts. They are actually grey - silver under it.
I can't tell for sure, but it looks like it could be one of the machines that parks the needle to the left when on straight stitch. Your stitch width nob has a little lever sticking out from it that I think would be a lock to set it at the width you want for ZZ stitches. "0" would be straight stitch, and then the larger the number the wider the ZZ stitch.
It also looks to use high shank feet. I could be wrong on that though.
Uses standard class 15 bobbins and standard 15x1 needles.
The lever at the base of the pillar raises and lowers the feed dogs for FMQ and darning.
A very simple machine to use.
By varying the stitch length and width you can make all kinds of stitches.
The two tiny rivets in the flat space to the right of where the
J- A 4 is stamped would have held a placard with the model number and brand on it. It looks to be gone. Without that the only way to know who originally sold it is to find one identical to it that's still marked.
Joe