It all started when the banquet of kings happened, where Iskandar, Gilgamesh and Saber discussed their ideologies regarding what it means to be a king. Some sort of admiration blossomed there in Gil towards Saber, which afterward led to unrequited love and was stretched to an extent where it almost becomes diabolical in a few of the aspects.
Gilgamesh was the first half god and half human to ever walk on Earth. In addition to that, he was destined to achieve feats that humanity wasn’t able to do before. He was the first king the world ever witnessed and proclaimed himself as the ‘King of Heroes’ implying that he is the origin of myths and models which the heroes were based on. Basically, he has the power to do anything because he is in the position to do so, almost making him the embodiment of a god.
On the other hand, there was Saber who believed that being good will lead to good things only. But her kingdom fell apart despite her being the ‘king’ chosen by people. In her life as King Arthur, she was unable to find the discrepancy which led to the fall of her empire and thus has regrets as a heroic spirit. She wants to redo everything again and undo the inevitable which comes along the way through the help of the Holy Grail.
Now, as we know that Gil just seeks amusement, a way to enrich his existence as a heroic spirit till the war ends but that amusement for a moment turned into admiration when Saber stated her views on kingship, her regrets and her cause for fighting.
Let’s see this situation from the perspective of Gil, he sees a woman who wants to change the inevitable past [to not pull the sword and to not become the king] which is going to destroy everything she ever stood for i.e. her kingdom and the people. This fascinates him, the idea of achieving something which is impossible for humans to do so, he likes it when a mere human tries to reach for something which was never meant for them. Gil admires the stubbornness of this sort, knowing that it’s just a futile attempt but also finding it entertaining at the same time.
It was that naive little wish of Saber which piqued the interest of the prideful king of heroes. To the eyes and minds of both Iskandar and Gil, Saber is someone who will fail her ideals regardless of whatever the circumstances are and yet she has the will to fight against the odds and the courage to hold her conviction. It was an act of idealism mixed with some chivalrous and headstrong thoughts. Also, she faintly reminded him of Enkidu, the only person whom he considered his equal and a dear friend.
It’s the thought that Saber could change her past of becoming a king is the only reason Gil genuinely admires her although he knows that it’s just a futile attempt for redemption but he finds it entertaining and wants to see how long her conviction will hold up.
For him, it equals to the meaning of daring to stand shoulder to shoulder with the Gods. Her unyielding naive idealism is the only thing which genuinely attracts Gil, the day she chooses to let go of her ideal, he will drop her without a second thought and be the pathetic prideful king he always has been.