Let's assume Eun Tak can't see the sword. How did she come to know about the tiger engravement, then? Did she read about it in that one book (shouldn't be written there so I doubt it)? Or did someone else tell her (I think goblin doesn't talk about that with others, so again, I doubt it)?
In the end, my conclusion is that she can indeed see the sword, but she makes us believe otherwise/doubt it.
She did get to know that if she manages to pull out the sword then the Goblin will "die" once and for all, right? (meaning his endless life will end)
Even if she can see it, maybe she just doesn't want everything to end and is afraid of that as well... just my guess tho

She said in the first ep, she thought his "blue" flames would be "cool" (temp wise), & then got surprised when they were hotter than expected. This happens when she grabs his arm in the library. How did she kno he has blue flame energy emenating from him to begin with, when he'd never let them show on purpose until she startled him? It sounds plausible to me, that she was ignoring the sword for various reasons (imagine how many other similarly injured spirits she's seen).. lol. 

Btw, "respectively" used in the context above means, "in that order"; ie "one & two = one & two", & as written it looks like a shortcut for "King = Sunny & Queen = Reaper", tho your following explanation implies you meant the opposite, lol. 

I'm really curious if anyone has any thoughts about the field of "lovers flowers", or any of my other ponderances, hehe.. 

Well, the queen had been killed first, before him (tho she sure was dying ~slowly, heh) so I think he would have already known she was gone.. especially since so many years (10-20ish) passed. But then the king must have still been fairly young at his own death- likely poisoned by his villainous adviser, etc. And surrounded by paintings of the queen.. hmm.

One of my fave moments was after WY confirms that reincarnation isn't limited to ~gender, KS seems to consider instant forgiveness if the king is now a "sexy" popstar girl, lol pfftt way to ~subtly assure the audience of his "hetero"ness, haha. Whaat. I'm surprised he didn't tell WY to go make sure, being that they both can teleport & all.. (now imagine KS dragging WY around- in invisible mode- to randomly check ppl all over the place, LOL since WY has to make actual contact with them to see)

I think she can see the sword but I think she won't be able to pull it out just yet. I think there is some other rule that we don't know about yet. Like maybe she can pull it out after he deals with his past. 

I don't think revenge. Just maybe there's a truth that needs to be found out about the events in the past and until that gets sorted then she won't be able to pull the sword out....