I'll list some of my personal fave "atypical" leaders (and I may do more if there's interest), with a word of who they are and why they are interesting
TAYTU BETUL (Ethiopia)
The adage of "Behind Every Great Man, There's A Great Woman" reaches its Zenith with Taytu Betul, the spouse of Menelik II. Menelik, who we know from his appearance in Civ6, is arguably the most effective Ethiopian monarch. Part of the reason for that was the support he received from his wife. Noted to be cunning, ambitious and difficult to please (as well as unwaveringly loyal to her husband and the country of Ethiopia), Taytu Betul proved herself to be a shrewd negotiator (it was she who scrutinized and then repealed the Treaty of Wuchale, which ultimately led to Italy's failed attempt to subjegate Ethopia and the Battle of Adwa), a capable leader (She commanded a battalion of her own troops in the battle of Adwa), and a woman of action as well as words (the new capital city of Addis Ababa was settled under her command). She was also a highly skilled player of Ethiopian chess. Additionally, as an ethnic Oromo of Muslim background, her marriage helped consolidate Ethiopia as a unified regional power. She was powerful (and annoying) enough for the Italians to launch smear campaign after smear campaign to villify her for her role in Italy's failed colonization attempt. In reality, she was just kind of really good at playing the game of thrones despite being black and female and some individuals found that hard to accept, I guess

. If consorts make worthy Civ leaders (and they are - as proven by Eleanor and CdM), she should be at the front of the queue.
VOLTAIRE (France)
France hardly has a shortage of great leader options. Charlemagne and Louis XVI, Cathérine de Medici and Eleanor of Aquitaine, Joan of Arc... and that's without delving into Clovis, Mazarin, Richelieu, Philippe Auguste, Vauban and many others. However, on this occassion, I will advocate Voltaire, a choice who is similar to the French as Benjamin Franklin is to the Americans. Like Franklin, Voltaire embodies the core values that made his country what it is - a political philosopher and prime advocate for liberalism, free speech and secularism, as well as a notable playright and satirizer, Voltaire
outfrenches any French leader choice, with his writings and political theories maintaining relevance decades after his death.
ARWA AL-SULYAHI (Arabia/Yemen)
The beauty of unclipping leaders is that several worthy choices become more viable. Arwa al-Sulyahi, who ruled the Yemeni Sulayhid Kingdom from 1074 to her death 1138, is a great example of this. Arwa represents the rare female monarch of the islamic world, with the even rarer distinction of being beloved and respected by her peers - allowing her to inherit the Sulayhi kingdom as its sole monarch after the death of her spouse (and before that as its defacto leader as her ineffective husband would delegate most of his tasks off to his wife). Her talents at governants, as well as her piety, earned her the distinction of being the ONLY female islamic monarch to have the khutbah (a declaration of dedication for the monarch that started islamic religious services at the time) proclaimed in her name. During her reign ,she patronized agriculture and send Shi'a missionaries to India, which in Civ terms makes her a natural choice for a leader who excels both at population growth and religious spread. Arwa passed away at the ripe of age of 90 and is to this day a respected historical figure in Yemen. (the university of Sana'a was named on her honour)
NUR JAHAN (Mughal India)
Another beneficiary of the "unclipped leaders" policy, is Nur Jahan, the wife of the somewhat ineffective Mughal emperor Jahangir, who kindly ran his empire for him. Nur Jahan is probably the most powerful woman in Indian history until Indira Gandhi, but is a more of less awkward fit for an Indian leader as she herself isn't ethnically Indian (not that "ethnically indian" isn't a Trump's Ego-sized umbrella term in itself, but I'm not opening that can of worms). A
Persian princess who married into the Timurid dynasty, Nur Jahan was born in Kandahar and likely spoke
Dari as her native language. She is nevertheless a fascinating character, worthy of Civ inclusion. As queen consort she was generous patron of the arts, taking a particular interest in apparel (she is credited to have created, or at least popularized several textiles, such as the Nurmanhali dress) and architecture (she built many sarais and gardens for weary travellers to rest in). She herself was a shrewd and effective politician with a penchant for hunting (her hobby of hunting tigers is well documented). If Ed doesn't know about her yet, he should do asap. Once he's done drooling over her wikipage, he can have
@Andrew Johnson [FXS] put together a case file on her, to prepare for her upcoming inclusion in Civ7's first post-release DLC.
ZHENG HE (China)
Like France, China has no shortage of excellent leader choices, and Zheng He is near the top of the list of non-monarch leaders, alongside Sun Tzu and the already included Confucius. Zheng He was a eunuch in service to the Yongle Emperor (whom we all know and love from Civ6), and is the most accomplished naval commander in Chinese's history. Zheng He's most notable achievements are the seven treasure voyagers he completed under the Yongle Emperor and his successor, bringing back riches and information, while flexing China as a naval superpower. Aside from his exploits, Zheng He also has an interesting backstory. He was a direct decendant of the Khwarezmian governor Kublai Khan established as governor of Yunnan, and yet helped the Ming conquer Yunnan from its Mongol owners. His friendship(?) with the Yongle emperor whom he faithfully served since his teenage years is also well attested. If we want a Chinese leader with a naval flavour who is also good at raking in money and earning science, Zheng He is that choice

.