If you’re integrating/being an “expat” in a society, you’re going to develop familiarity. The “average” Korean won’t know anything about you and continue to just treat you like a tourist (unless you speak fluent Korean), but your social and professional circle won’t. You can’t go very far into relationships in a foreign country without people knowing your background.

Less importantly but somewhat obvious: many Koreans are fairly competent in English and familiar with common American accents. They’ll know pretty quickly if you aren’t speaking with one.

language/accent obviously, dress, manners and also English people in particular look distinct physically given that most white Americans are more likely to have Northwestern European ancestry. The stereotypical "American white guy" would have an easier time on Swedish or German TV than joining the cast of Peaky Blinders

Isn't this like saying it's impossible to see the difference between a Korean person or a Japanese person speaking English? It should be fairly obvious from the accent alone.