Tim never really liked Jason. When he first saw batman and Robin (Grayson) it was a constant that he doesn't want to change, the sudden introduction of Nightwing is something but a new Robin—a more impulsive Robin—is something that leaves a bitter taste in his mouth. He gives out reasons back then like "I just prefer the old costume." Or "he fights too rough than the previous Robin." To anyone who would've asked him his opinions at the time. He couldn't deny though that if The first Robin was sunlight, this one was the sun itself, he was a star that burns when touched, he was light, and much like his predecessor, he is hope.
When Jason Died, the city lost a star, and batman lost a child, taking his chance Tim took the role of Robin because Batman needs a Robin, but he was dealing with a grieving father not the capes crusader he saw in those pictures. He was dealing with a different batman, and so the line that connects the two Robins is one of animosity, well at least in Tim's end.
When he returns back from the dead the hate is still there but only tenfold, the fight in the Titan's tower doesn't help too. Tim now sees a shell of who Jason is back then, but now he could tell that their eyes reflect one another, both out of hatred. Some are towards the other but most of it is towards themselves, both of them are trying to prove that they're good enough, Tim for the Mantle or Robin and Jason for living. Both never really got their answer right after.
What changed though is when Damian comes in the play. It was just about a few days since Jason revealed himself and just about two weeks since Bruce finally accepts Tim not just Robin but also as his son. Damian though has his blood to back him up, he is the blood son of batman and was groomed to be one. At least Jason doesn't want the title of being a Robin anymore but Damian? Damian is Ready to fight for it if he needs to.
A few months after, This leads to him sneaking out of the manor, and soon being face to face with Jason (without the mask) as he sneaks in the manor. The two might be going on separate ways but both of them are doing it for the same reason. It's because both of them don't feel like they belonged in this house. Tim quickly breaks eye contact and leaves before any of them utter a word, it's probably just gonna be another argument anyways.
Tim moves more closely to the shadows without his uniform on, he sneaks his way through Gotham's nightlife till he reaches his destination when he can finally breathe. He sits and lets his back rest at the ledge of its rooftop. He tries to capture something with His camera before being started by a bag of local fast food thrown into him. He quickly looked from his right to find Jason, hands up in a surrendered pose. Tim admits that he was pretty much preparing for a fight anyways.
"did you track me down?" He starts to ask.
"I guess Bruce was right about your deductive abilities." Jason speaks now sitting next to him, well as close as he can be for now. "You look malnourished, that's such a bad image for a billionaire's son you know that?"
Tim grumbles and takes the burger from the bag, not before thanking Jason, he still has manners after all.
After a pause it was Tim's turn to speak. "You seem awfully passive today."
Jason grumbles "just....tired."
"...you can say that again" Tim mutters below his breath, though he was pretty sure Jason still caught that.
It feels weird being like this. It's nice to get along with someone at least after all of what just happened but Jason? Past Tim would've laughed at his face and would've probably asked if he died too at that point.
"...I've known him, that kid ever since he was an infant" Jason says, it feels so calm that Tim was pretty much unnerved by it. "He's like me and dick, we had nothing. He feels like he's nothing until he takes that damn symbol off on you."
Jason lowers his drink. "What I'm saying is, you're different." Tim couldn't tell anymore if there's still any malice present in his voice. "We all know nothing but to be Robin, but you, choose to be a Robin. You can still be the boy wonder but you're also Tim fucking Drake." A series of beeps cut him through whatever he's about to say, Jason grumbled and muttered something about therapy appointments or something before putting back his helmet on. "Just think about what I said Tim." Was the last thing Tim heard before the other just disappeared through the night.
It was that night when Tim finally realized why Jason is seen as a light.
Damian is annoying but after that encounter he became a tad less of a worry and more of a grievance. Most of what they do still ends up in fights (physical or otherwise) but it also makes him realize that he can still accept Damian as Damian. After Damian takes the title of Robin, it was more so less of despair and more of just a wistful sorrow for Tim. Times when Dick is unavailable with Damian he would just Mostly hang out with Steph in their free time.
Jason though, is always the second option other than Steph. He is more respectful towards Jason now than he was before. Making less insults and more so just letting him linger in the manor as much as he can. He knows what Jason needs is someone who accepts his presence and he's just fine doing just that. This just gradually formed their relationship to what it is, light banter, teases about pretty much anything, and trying to be competitive. Jason as more and more he frequents the manor the more Tim actually considers him more as his brother.
And even in their darkest moments, the world feels more brighter than before because of it.