I am thinking about @taxinealkaloids Gertrude and Elias artworks again (🥰😍💖) so I decided to put my thoughts regarding these two into words instead of only rambling around in the tags, so here we go:
I think a big aspect of their relationship is some kind of curiosity. I think they were both very interested in each other, always curious to find out just how far the other was willing to go. Finding out where the line is, testing if the other would snap. And I think they both immensly enjoyed it. Was that the reason why Elias never used his powers on Gertrude? Because he wanted to see, to experience for himself just how far she would be able to go? And vice versa, was Gertrude curious with just how much stuff she could get away with before Elias intervened? She killed assisstants left and right, kept the entire archive in disorder and got away with it every single time, Elias even encouraging her in some cases like with Emma. But the line was drawn the moment she tried to set the archives on fire. That must have been so exciting in a way for them both though? After years and years of testing each other, trying to get under each others skin they finally cross the line, both of them do. He didn't expect her to actually do it, he didn't expect her to find out about his secret, about the panopticon. And she didn't expect him to actually kill her. Honestly, how exciting! They finally know where the relationship they have with each other ends, and it ends with Gertrude's death. A death she for sure didn't see coming.
What also interests me a lot in their relationship is the fact how similar they are percieved by the people around them? When we hear mentions of them in the early epsiodes it is always clear that they are definitely not seen as being good at their job. Jon is pissed that the entire archive is in a state of absolute chaos, and he mentions more than once that he doesn't think Gertrude was a good archivist. Same with Elias, Tim mentions a few times that Elias is incapable of ruling the institute properly, and Jon says a few not so nice things as well. They are both presented as being utterly incapable and bad at their jobs until more and more things come to light. Until it turns out that they both aren't actually really bad, in fact they are quite good at what they do. Until it is clear that the Archivist position isn't actually am Archivist position in the original sense and until it is clear that head of the institute actually means something else than the head in a traditional sense. And after all, she wanted to stop rituals, which she did quite successful until she tried to stop Elias and Elias himself? Oh boy, he was absolutely excellent. Preparing Jon for 4 seasons, carefully planning everything, making sure Jon is at the right place in the right time...amazing, showstopping, incredible. And well, all his plans succeeded actually? Jon got marked and Jon read the letter and Jon brought the apocalypse and Elias himself ended up in the center of the eye, caught up in pure bliss and knowlegde. He got everything he wanted. So they both were actually very successful, just not in the original sense of the jobs they were doing.
What I also really love is how they both are seen as absolutely harmless on the outside but can both go absolutely feral if the need be. Like I first thought of Gertrude as a little old grandma, in Tim's words "more cardigan than woman" and I would have never in a million years guessed that she would turn out to be a very cold hearted person who had absolutely no problem sacrificing the lives of her assisstants for her agenda or even killing them herself if need be.
Same with the King himself, Elias is always calm. Always. There is an attack on the institute? Well, none of his business really? Idk but if you all insist, well then, let's help them I guess. Elias was calm when he was arrested, he was calm when he told the others about his crimes, he is always calm. And then he goes and shoots Gertrude not once, not twice but three times. He bludgeons Jürgen Leitner with a giant pipe. Again, he doesn't hit im just once. And then he goes back to being absolutely calm again, like nothing happened. (And Johnny wrote this character and then expected people to dislike him? to not find him absolutely hot? wild) So yeah, they are both percieved as harmless and even a bit dumb until their true faces appear and then it is clear that they aren't so harmless after all.
And to end this ridiculously long essay, one last point: I like to think they share the same sense of humour. Like I don't have any quotes to back this up, I just think they give off the same vibes regarding that. Like he makes "I see" jokes all the time and I guess if he had told Gertrude about Barnabas letter and the bones still in his office they would have had a laugh about this, I am sure of it.