There are different types of THAT clause.
1. I think that she is from korea. (like your examples)
This "that" is not very necessary. Very often, people just don't say it. No need to pause.
2. The language that you grow up speaking is Korean.
This "that" is optional. If you really want to pause, pause before "that".
3. I like the horse that ran the fastest.
This "that" is necessary in the sentence. If you really want to pause, pause before "that".
Im not native though. Hopefully there will be better answers.