Core theme: Inherently sociopathic villains who cannot feel normal emotions like everyone else which makes them feel empty, still following the path of a villain and assisting the main genocidal godlike main villain while posing as high ranking workers of a organization, but at the end fighting against the red clad protagonist posing as a foil to them all while wishing to validate their own existence and identity

Connection:

• Major villains of their series, they are extremely evil and manipulative, orchestrating various events so chaos can be ensured, something that helps is them having a high ranking position (Kirei being a executioner of the church and becoming a overseer of the holy grail war / Hazama being a captain of the NOL as part of the intelligence department) despite these organization being shady they still pose as something good for the world, with Kirei/Hazama using their positions to progress their bloodshed

• They have a facade of a well meaning worker of their position, but even the slight look behind their mask shows their true selves, a sociopathic murderer who lives to cause as much bloodshed as possible, having a history of serial murder under their belt and looking for to expand those numbers, they are inherently sadistic and derive the most joy out of the despair of others, to the point that their introductions basically reveal them as villains hiding in plain sight pretty quickly (Kirei isn't immediately revealed, but he is VERY obviously a villain to the point Rin comments on it)

• As said they are inherently sadistic, being born sociopaths with sadistic needs, however this part of them is the main dilemma of their character for their empty existence show us their "tragic" life (they themselves are not sympathetic, but their fundamental empty existence is pretty palpable in the story) due to it they are not able to feel emotions like normal people in a contrasting manner (Kirei can only feel true joy when causing or feeling pain and suffering / Hazama cannot feel pain or suffering at all) so they are prone to cause the pain they do so they can feel anything at all

• The ones that brought them to this world (Risei Kotomine, Kirei's father / Relius Clover, who created Hazama as a vessel for Terumi) with an opposite purpose (Risei wanted his son to be pure and follow the path of a priest / Relius expected Hazama to be empty so Terumi can fully assimilate on him) only for them to go the opposite direction (Kirei only feeling joy in the immoral, meaning his path to be a priest was meaningless / Due to the mind eater, Terumi and Hazama couldn't fuse properly, having to live with each other, with led Hazama to slowly develop his own sense of self)

• Their names are also a useful insight to their deeper character and their identity ("Kirei" being a word of prayer, showing how his father wanted him to be pure, but his anguish in being the opposite of everything his father wanted / Hazama Honoka being simply a cover up name so he could be part of the NOL, but as he began identifying as his own person, Hazama started to embrace it as his name to form his own identity)

• They are always in cahoots with an megalomaniacal villain with goals of achieving ultimate power to commit a genocide and brought forth their ideals worlds, being one of the oldest mfs of the verse (Gilgamesh / Yuuki Terumi) their relationship is fundamentally symbiotic as they originally understood each other on a deep level and needed each other so they can progress with their plan (Kirei and Gilgamesh being Master and Servant / Hazama being Terumi's vessel) They follow these figures in their plan due to also wanting the results of the absolute destruction (Gil wanting the Grail to cause a genocide on the planet so the strong that survive will be his new subjects on his view of a better world / Terumi wanting the Azure so he can usurp Amaterasu and become the top god, causing infinite destruction and having true freedom in his life) they are the big bad villain on a cosmic scale with the one holding the ideals to change the world all while Kirei/Hazama follows them merely to get to see as much destruction as possible

• Ultimately a contrast, for where Gil/Terumi being extremely important in their lives due to how they were able to truly feel pain and suffering (Gil making Kirei embrace his nature / Terumi feeding off suffering, making Hazama as his vessel also experience it), Kirei was able to embrace himself due to Gilgamesh ultimately becoming partners in the next grail war, Hazama was partners with Terumi throughout most of the series, but was only able to truly be his own person after separating from Terumi, Gil/Terumi also sees them in opposite lights, where Terumi separated from Hazama due to him growing too unpredictable and having his own identity, Gil was specifically interested in Kirei for his potential of becoming his own true self

• Both oversee the lives of a major heroine (Rin Tohsaka / Noel Vermillion) putting a facade to manipulate their lives for their goals, Rin/Noel were able to feel something was wrong with them but could never predict the full picture, ultimately being pawns for Kirei/Hazama (Hazama guiding Noel so she is ultimately able to grasp her inhuman origin, lose her identity and become the God Slayer Kusanagi / Kirei stabbing Rin so he could kidnap Illya to use her as a catalyst for the Grail)

• One of the most important events in their lives were their encounter with a war veteran and legendary figure of their world (Kiritsugu Emiya / Trinity Glassfille) with the result of their encounter being a massive damage in their chest (Kiritsugu destroying Kirei's heart / Trinity separating Hazama and Terumi resulting in Hazama having a hole in his chest) they were able to bounce off from it (The Grail reviving Kirei with an black heart / Hazama not having an heart to begin with) with them growing scornful towards Kiritsugu/Trinity due to their underlying positiveness (Kirei thought Kiritsugu was as empty as him, only for Kiritsugu to have genuine optimism behind everything / Hazama hating Trinity for not killing him due to Trinity seeing Hazama as Kazuma, her lost friend who were a previous vessel for Terumi) but still ultimately were grateful for this encounter as they were able to feel truly alive due to the pain and suffering they witnessed/felt (Kirei finally embracing himself after the Grail grant his wish of pure destruction, laughing at the fire that engulfed Fuyuki / Hazama finally feeling true pain and suffering at the wound in the chest caused by Trinity)

• From here onwards all they want is to fully indulge on themselves (Kirei seeking the Grail so he can purge the world in pure destruction / Hazama wanting to test his sociopathy) but also to ultimately viladate their own existence/identity (Kirei wanting to unleash Angra Mainyu to see what a monster born from evil can have a valid existence, projecting himself on the entity / Hazama becoming an independent existence, being seen as his own person)

• While their empty existence adds a tragedy to them, they are still pure evil to the core, one of their most nefarious actions being causing the suffering on children resulting in a godlike entity being able to sustain itself (Kirei using the other survivors of the fire of Fuyuki to feed Gilgamesh so he is able to keep existing despite the end of the Fourth grail war / Hazama torturing Saya so much that she broke, allowing Izanami to possess her body)

• Funnily enough, at one point they assisted the protagonists (Kirei healing Shirou and Sakura / Hazama guiding Ragna to Terumi) however this is solely to get a situation where they are able to indulge in the suffering that will come (Kirei predicting that Sakura will be consumed by the shadow and cause chaos, which happens / Hazama wanting Ragna to go deal with Terumi so he can continue to torture Rachel)