I looked into the exact mechanics of perfect pivoting a while ago and it's like you guys say, it revolves around the initial dash frames.
I'm pretty sure, without testing literally every character (which anyone else is free to do btw), that every character has the exact same amount of initial dash frames. So using any character as the example, you need to hit the joystick either left or right to initiate the dash, then, assuming for now that you hit the joystick in the direction your character was already facing, on any frame following that up to frame 6, you must hit the joystick in the opposite direction but only for one frame. So for example, to do the longest PP, you dash, and on the 6th frame you hit the joystick backwards, and by the 7th frame the joystick must be returned to neutral, otherwise you'll dash back in the other direction. If instead you hit the joystick backwards on the 7th frame you'll go into the slow dash turn animation. Note that dashing in the direction your character is not facing will give you an extra frame to work with because the first frame will be a pivot, then the second frame will be the first frame of the initial dash.
I'm pretty sure, without testing literally every character (which anyone else is free to do btw), that every character has the exact same amount of initial dash frames. So using any character as the example, you need to hit the joystick either left or right to initiate the dash, then, assuming for now that you hit the joystick in the direction your character was already facing, on any frame following that up to frame 6, you must hit the joystick in the opposite direction but only for one frame. So for example, to do the longest PP, you dash, and on the 6th frame you hit the joystick backwards, and by the 7th frame the joystick must be returned to neutral, otherwise you'll dash back in the other direction. If instead you hit the joystick backwards on the 7th frame you'll go into the slow dash turn animation. Note that dashing in the direction your character is not facing will give you an extra frame to work with because the first frame will be a pivot, then the second frame will be the first frame of the initial dash.