When under the effect of Hide, Huton's timer is paused that way when you use it at the start of a Trial or before a boss you don't have to worry about refreshing it before someone charges into battle (since countdowns only usually happen in Statics).

This way I can setup my Huton at the start even when it turns out someone is watching a cutscene or the tanks are taking their time without worrying of refreshing and then the tank suddenly charges in and I can't use Hide anymore to reset Mudras so I have to start with one down.

And no, Huraijin is not the solution to that.