I'd avoid relying on a timing tell without ample evidence to support it as a real tell. Online timing is too easy to fake...and some folks get married to their hands and have made a decision no matter what yours is. I fake timing tells in my home games sometimes as a way to encourage the fold. (I'm pretty sure they think they've read it as an AA type tell... I sometimes do it in my LIVE home games too...to the same effect.
I wartched a Doug Polk video very recently about folding KK. Theses were all instances where people folded KK and Doug reviews whether he thinks it was a good fold or not, and what the result actually was. (And you can play along as you don't know the outcome immediately).
Here is the link: Should You Ever Fold Kings Pre-Flop?
-- Doug Polk Video (You don't have to like him to learn from him!)
For me, the biggest thing is the type of game I'm playing. the higher the stakes, the more likely I am to be more thoughtful about pre-flop folding of premium made hands. I tend to rely on a lot of intel, so early game, I'm not playing much...just figuring out what types of players I'm up against. (I'm still up for a shove or a call early on, provided there are rebuys available)... I'd tend to play those KK almost every time early game...but later on...if the intel was building up...
But in general, folding KK is a rarity for me. I've only done it a few times and every time was EITHER around the bubble with a healthy chip stack or when there are already a bunch of folks shoving into a pot on a final table -- so I might fold there in order to guarantee a ladder up.
What I would say though, with KK...you're more likely to have fewer losses if you see a flop before shoving KK. No mater the hand, pre-flop shoving is a bit gambly and isn't really playing poker to extract maximum value.
I often think people are so focussed on aggression in poker, that they forget that the real name of the game is getting better value per hand than your opponents. Pre-flop shoves, too often, result in getting blinds only, or -- in the smaller stakes -- multiway shoved pots...and you do not want to be there very often. The real question here is -- are you able to be better at playing KK than the rest of people? To do so, you MUST have at least some situations where you are willing to fold almost any hand.
I maintain that folding is the most important skill in poker...and it is one that I've not yet mastered however...but I'm working on it!
All the best.