I can’t decide on anyone in particular, but I can totally see all the shinobi wanting to challenge one another for fun & to test their skills; and I can see them all sneaking around the village pulling off very risky dares, trying to see how much they can get away with without getting caught.
The Hokage totally knows that their shinobi get up to mischief at the end of the year, but as long as it’s harmless and non-destructive & stuff, they can get away with it (not that the Hokage would ever say so!)
I feel like it’s something Iruka & his friends would have started in Iruka’s pransker days, and it’s just spread & grown, becoming more and more ridiculous each year.
And writing this, all I can picture is Yamato sneaking out to the Hokage cliff, and using his earth style to carefully move the Hokage faces a little to the side without being caught; and because he’s really good at being stealthy, he doesn’t get caught, so when people notice, they are very confused because they nor anyone else had noticed anything, and surely at least one person would have detected a jutsu being cast for something like that.
After some time, Yamato puts everything back to normal (or maybe he just leaves it out of place for a day, then puts it back to normal the next day); and when he starts doing it every year, the mystery sparks rumours about who’s doing it, and even some kind of urban legend, with some people saying that because no one has ever been caught, the faces have to be moving on their own XD
The only other person who knows is Kakashi, because he would definitely have to figure out the mystery; and he would do anything to find out XD (Or maybe Yamato is too stealthy for even him, and Kakashi’s yearly tradition is to figure out the mystery of the moving cliff faces, because it is driving him crazy not knowing, while Yamato desperately tries to throw him off is trail & avoid him)
Kakashi trying to get to the bottom of why the Hokage faces move once a year, every year 
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