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Your situation will remain the same no matter were the income is earned. As a US Citizen you will continue to report the worldwide income on your US return. You are allowed to use the Form 1116 for the taxes that you must pay to Japan as a Resident there. This does not result in double taxation but double reporting , yes. You may use the Form 2555 to exclude your earned income while residing in Japan. This will allow you to exclude the earned income but to use the Foreign Tax Credit for the capital gains, just make sure that you do not use the tax paid for the earned income on the Form 1116 also since you are not allowed to claim a tax benfit for the earned income in 2 ways. Pick and choose which works best for you when it comes to the earned income. You can use Form 2555 or the Form 1116 for the taxes you paid in Japan for the earned income but not both.Your last question is the most complicated. Japan has a pay at source requirement so if you becoame a nonresident you will have tax withheld when the sale occurs. The US and Japan does have a tax treaty so if you have withholding as a nonresident and the capital gains came from a Japanese company you could file in Japan and use the traty to avoid tax (or pay a lower rate) in Japan.
Regarding my taxes paid to Japan on capital gains from gold and silver bullion sold in the USA, my main issue is can I get a Foreign Tax Credit (Form 1116) or only an Itemized Deduction (Schedule A, Form 1040).
Looking at the Foreign Tax Credit Form 1116 for "Passive category income" it says, "Part I Taxable Income or Loss from Sources Outside the United States (for Category Checked Above)". My capital gains came from precious metals sold in the USA, not from "Sources Outside the United States". Would it be correct to assume that you can get a foreign tax credit only for income earned in a foreign country (such as Japan) on which you have paid taxes to that foreign country (such as Japan)? In contrast, I earned the income in the USA, but paid taxes on it to Japan. How can I get my American income taxes credited against my Japanese income tax? I need the Japanese government to give me credit for foreign taxes I paid to the USA.
Because you paid the foreign tax in Japan you can claim the credit against the US. You cannot claim a credit in both countries. You will need to choose which country gives you the better tax benefit from the foreign tax credit.