Here are a few readings on Korea/U.S. relations from the 1800s. There is no agenda in presenting this, aside from sparking some interest in looking at history as much as current affairs. There are multiple views of these events, many more than I have offered links to. History is not fact, it is interpretation, selection, and isolation of specific aspects of fact, culture, viewpoint, access, knowledge and emotion – so always seek as many views on an event as possible. This is barely a start.
Excerpt from "A Brief History of the US-Korea Relations Prior to 1945"
Report of the Secretary of the U.S. Navy on the General Sherman Incident, 1867
1871 U.S. Korea Campaign
U.S. Medal of Honor recipients from the 1871 Korea Campaign
The First US Naval Attaché to Korea