-었다가 is the past form of -다가 I think you have the meaning right, but the problem your having seems to be deriving from the difference between English speakers and Korean speakers in the perception of what is considered "past." For Koreans, "past" does not necessarily have to be long ago. Not that English speakers use past tense only when the event occured like days ago, for Koreans, if one action is finished, it is considered past. See, '불을 껐다 켰다 하지 마세요.' in this sentence, English translation would be 'Don't keep turning the light on and off,' whcih does not include even a hint of past. But when you imagine the situation, you cannot turn off the light while turning it on. When you click the switch, it turns on or off the light instantly. There is no time gap between your pressing the switch and the light turning on. (If you say 불을 키다 끄다 하지 마세요, which would be the present tense, it would be like you are pressing the light switch just half the way when you stop pressing, which would be quite unnatural.) In short, because when the person turn off the light, the light has already been turned on, so its action(turning on) is considered finished and thus past. 그분이 계속 왔다 갔다 하세요. Is not so different. If the person(그분) has a destination and try to reach it, and then stops and comes back, it would be 그분이 계속 오다 가다 하세요. But in the sentence, it seems the person (그분) does not have destination but just moving this way and that because he is nervouse or boring or something. So because he does not have any specific destination, when he stops moving closer(오다) the action of coming ends and thus considered finished. And the same happens when he goes(가다). So, 그분이 오다 가다 한다 makes perfect sense too. Just that its meaning is different from 그분이 왔다 갔다 한다. The former implies that he has a destination while latter implies that he doesn't have one. But you can't say 불을 키다 끄다 한다 because there is no 'in middle of turning on the light.' I hope this could help. I know how frustrating it is when you just can't grasp why the heck the natives are saying the way they do.