You should have the chance to make a wish list but it will always be at the needs of the Army, so if the needs of the Army match your wish list then it may happen, but there is no guarantees.
Check out these threads:
If you want to be stationed somewhere else, there are only a few ways you can make this happen, and then, maybe.
The first is re-enlist and request a specific duty assignment. If there is a slot open for your rank and MOS, there is a chance you may get the assignment you are looking for. If there is no slot for your rank and MOS, then you will not get it as part of your re-enlistment. Since you are already active duty, the wish list, as mentioned by Revdeck, no longer applies. If you are within one year of your ETS date and you do not want to re-enlist, you will be classified as a "surplus soldier" after you re-deploy to Germany and there will be no chance of being sent to Japan.
You current assignment length requirements at your current duty station must be met before you can realistically think about being sent somewhere else. You can find out the details for OCONUS assignment lengths by contacting your unit retention officer. As a general rule, in order to be transferred, you must complete the term length of your current duty assignment.
Since you are deployed, I would suggest contacting your Branch about 2 months or so before you re-deploy back to Germany. Send an email or call your branch and follow up about once a week until you get an answer. I suggest that you do not pester your branch. Then again, the "squeeky hinge gets the grease." Proceed at your own risk in terms of how often you follow up.
I hope this helps. Good luck.
To add a caviat to what SPC VonOot said, the most surefire way to get it is in a reenlistment. Since you'll have to go through your career counselor to reenlist, that's your first place to start. Fair warning though, your career counselor only sends the request up through branch anyway. If branch really doesn't have anything available, that's really about all you can do. If you're not in your reenlistment window right now and have at least 24 months time in service remaining, you can try contacting your branch manager and seeing if you can get an assignment. WARNING: most branch managers dislike hearing from Soldiers randomly jockeying for some assignment. Granted, they get it all day, but if you want to get started off on the right foot (and increase your chances of getting what you want), you should do it a certain way. I went through my NCO support channel and asked my team leader and my first sergeant if I could contact branch and what I was hoping to get. They gave their blessing and the first thing my branch manager asked when she answered the phone was who I was and if my CoC knew I was calling.