My wife is active duty Air Force and was given orders to Japan; I am in the Army reserves. Can I move with her?

Yes. Talk to your career counselor, she'll get you in contact with a unit over there, and you can continue to drill.

There are numerous IMA positions in Japan. You could look at getting one of those.

As long as she has "Accompanied" orders, yes you can. Now, being that you are Reserves, your options will be that you can either find a Reserve unit in that region with your MOS, enter the IRR for a spell, travel back and forth to your current unit, or you can RST with a unit that is willing to work with you on this. Step 1 for you is to get with your Career Counselor/Retention NCO and see if they can find a Reserve unit in Japan with your MOS.

you should be able to request a form of transfer from your leadership and given your case it should almost certainly be approved my buddy was in the guard down in florida and due to family matters moved to a different state and his transfer process was relatively smooth good luck

If she is authorized an accompanied tour and you are on the orders. You may be able to transfer to an overseas reserve unit in Japan or Korea. I knew many Army Reservists in Korea that lived in Japan. Contact a unit there and see what they can do for you. You may be able to work out constructive credit.

I recall (mostly Navy) but would presume there's a number of Army reservists out in Japan when I was frequently going there. They tended to be in "augment billets" and would drill with an active assigned unit. Their reserve command may be located in CONUS but that's just to cover the administrative stuff. There were few reserve units because the numbers could fluctuate and it's hard to stand up a unit without a consistent mission and staffing. Just remember your unit can be anywhere and your drill can be anywhere if that's how it's set up. Had several reservists doing their thing in Singapore, and Japan has much more opportunity. Your skillset looks interesting though. Public Works outfits are lead by MIL officers but the work is done by GoJ sponsored civilian employees and contracts, especially the later by contracts. So don't be surprised that what you do isn't exactly in your swim lane.

You can move with her. You just need to speak with your CoC to see what options you have in continuing to serve. There might be a unit in Japan you can drill with.