The greatest trick GRRM ever pulled was using a single act in the beginning of book one to convince the reader that Jaime Lannister, the biggest procrastinator this side of Rhaegar Targaryen, is impulsive.
Even defenestrating Bran isn’t truly impulsive. A quick decision, sure, but an impulsive act is one that is performed in a moment when it could’ve been delayed until further consideration could be given. So, a bad choice? Sure. But it isn’t like he could’ve put off killing the kid until later on.
Same with everything else he does. Going back for Brienne? A considered choice performed within the available time limit. Leaping into the bear pit? Same.
This is a man who spent fifteen years knowing Robert was abusive, yet did nothing to stop him. True, Cersei asked him not to…but wouldn’t an impulsive man have done it anyway? Sometime over those fifteen years? A man who even as a teenage boy waited well over a year, until the last second, to kill Aerys…and even changed clothes to do it. A man who waited until the last possible second to bust Tyrion out. A man who hangs around King’s Landing pretty much watching the Kettleblacks humping Cersei’s leg and does nothing. Who finally gets Lancel, the “other man,” alone, and instead of attacking him listens and counsels and tries to get him to eat something and encourages him to get out there and live his life.
Now Cersei? She is impulsive. Falyse and Mr Falyse, go kill Bronn for me. Oh no, Qyburn, here’s Falyse for your vivisection needs. Oh hey Qyburn send Falyse back I have use for her. This pattern - decisions made in the moment based upon whims that she forgets she even made at all and then when the whim turns out to have been a massive fuckup she covers up with even more impulsive bad moves - repeats for her. But Jaime is not this way. This is yet another of the million ways Jaime and Cersei - who are truly nothing alike - differ.
The only truly impulsive act I can remember seeing from Jaime Lannister? That one time he busted Red Ronnet Connington upside the head for trash talking Brienne. The Golden Bitchslap was performed without thought or planning and did not have to happen.
But other than that? Nah. This man is not impulsive. And to be fair, though he waits until the last second, unlike Rhaegar, he does know when the last second is.