I've stumbled upon this article and found out...
Daum: Korean. Also unsure about this one’s independence.
While they are not really well known outside South Korea, it has Wikipedia article and is one of the first search engine in Korea. I don't have much insight on how their search index is run, but they run their own index with own webmaster tools, site registration site (Korean only), and robots.
They once worked with Google (well, in 2000s) for their non-Korean index but their deal (seemingly) expired in 2009 and runs their own index.
One thing to note is that both Daum and Naver is (just like Google and Microsoft) owner of their own content services (ie. they both have blog, forum, and video platform) and are known to prioritize result from their own services over the answers available outside their walled garden.