I would absolutely love to! I'm glad I have an excuse to brainstorm for them.
We know so little about either of them, especially Tenn. Mostly making things up.
Tenn was born in the same birthing hall as Zim, Skoodge, Red, Purple, Gashloog ect, moments before Horrible Painful Overload Day pt 1 began. Their section of the smeetery is rather distant from the mother (green) brain, stationed at the heart of the global smeetery. Usually the smeets born there grow up to be shorter disposable foot soldiers or service drones.
Tenn was often mistaken for Zim as they appeared identical as smeets and she was occasionally punished for his misbehavior. She would sometimes agree to be a distraction for Zim as well in exchange for snacks or later called upon favors…which Zim often backed out of.
Tak was born on the other side of Irk in one of the “good" birthing stations deeper underground (warmer, bigger care drone staff, better maintained and closest to the mother brain.) Usually the smeets born in the good halls grow up to be taller, higher ranking soldiers, invaders or even tallests. Tak however always remained on the shorter end of average, which motivated her to constantly work harder/ improve.
Due to the massive power outrages following HPO day part 1 it was easy for Tak to slip away from her information hub. She would often sneak into the mother brain's chamber. She would stand in the cold green glow of her eyes and chat with the mother brain. The conversations were very one sided; the mother brain never acknowledged Tak, but she never alerted the care drones to retrieve her either. Tak used to believe she and the mother brain shared a close bond. Tak later concludes that she was too small for the mother brain to notice or too small to dignify her with acknowledgment.
Tak and Tenn did not physically meet each other until they entered advanced elite training on the planet Devastas. Tak was actually in a romantic rivalry with fellow soon-to-be invader Zee at this time. They competed for highest stats and praise from their commander. They caught the attention of their peers and TvZ were considered local celebrities.
Tenn was a nobody in the academy. Good enough to be enlisted, but struggled to stand out. She especially followed the Tak v Tenn rivalry closely, studying both their combat techniques and off campus chemistry. Tenn was insanely jealous, of Tak especially; not in a malicious way but in a pining, admiring way. Tenn wanted to BE Tak at that time. Being with her never occurred to her as an option.
Eventually Tenn's stats climbed to equal that of Tak and Zee's. She was pitted against Tak in a battle simulation exercise. Tenn defeated Tak by a thread. The two of them became friends instantly.
Tak started inviting Tenn to join her and Zee on snack runs, cozy couch breaks and Miyuki fan club meetings. Zee noticed a strong chemistry between the two of them. She gently pushed Tak and Tenn together and they have been an item ever since.
As far as head canons about Tak and Tenn individually.
Tak is overly competitive and can become obsessively vindictive (hence the case between her and Zim). Her attempts to foil Zim have put a strain on her relationship with Tenn (who is just naturally more laid back). It has lead to heated arguments between the two.
Tak adores Tenn's thick emerald lashes. The two of them have perfected butterfly kissing.
Tak is VERY protective of Tenn. She is aware Tenn suffers from a lack of confidence. She likes to push Tenn to build her up, but often causes Tenn anxiety instead.
Tak's trademark display of affection is teasing, but she has learned to dial it back for Tenn, as she can only handle so much teasing/ has trouble dishing it out herself.
Tak rarely cries. She usually cries only when alone. Tenn is the only living Irken to see Tak break down into tears.
Tak strives for excellence. She works well under pressure. She is innovative and creative, but can sometimes overestimate herself (or underestimate others).
This combined with her inability to let a grudge go is her biggest downfall.
Tak, unlike Zim, will not begrudge an Irken for outdoing her, IF she is convinced her opponent defeated her fairly. She HATES to be cheated.
Tenn is much more patient than Tak. Her greatest strength is her ability to pinpoint weaknesses in the strategies of her opponents/ enemies. Tenn can be an over thinker at times. She rarely takes risks. She is much more passive than Tak and rarely start conflicts, however she will engage in conflict when directly ordered.
Tenn is used to maintaining control over herself/ her affairs. On the rare occasion she loses control, she does panic.
Tenn learned a form of deep meditation during her attempt to invade planet Meekrob.
(After the events of Top of the Line) Mimi is destroyed (accidentally) by Gir's antics, giving Tak further reasons to despise, hold a vendetta against Zim.
Tenn is relieved when her mission failed and the tallest demote her to service drone. Tak is denied any chances of ree-enlisting with the Irken military, permanently encoded as a service drone and is EXTREMELY bitter about it.
Tak's love for Tenn eventually does outweigh her hatred for Zim.
I head canon that Tak and Tenn’s relationship is a slow building polyamorous one, hover they remain a constant duo.
(Icould go on, but I should probably stop XD.)