You're going to need to maintain a U.S. address or use the address of a trusted relative that resides in the U.S. while you reside in South Korea. Further, I use my U.S. cell phone whenever I call my U.S. brokers even though I primarily reside in Québec Canada but I use my U.S. home address for opening a broker account or anything financial...never my Québec Canada nor South France home address.
After your account is open, I don't think it matters with that specific broker. Thus, you can move or pretend you've moved to South Korea when in reality it's your primary address.
I think it doesn't matter because they already have verification from you about your U.S. citizenship, social security number, etc. Thus, after your account has been approved...they don't care where in the world you reside.
P.S. Stock brokers are less picky than Futures brokers about the residing address.
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