It would depend on what is happening in the story. This is no different than a DM who has an exact time for short rests; they are still making a judgement as to whether X minutes will occur according to the imperatives of the story and then giving that decision to the player. I just make the ruling without worrying about whether X minutes has passed (which will be a made-up number anyway) and just give them the information they care about: do we have time to take a short rest and still have the spell effect going.
Specifically timed short rests lead to weird results because, outside of combat, D&D adventures run narratively, not on timed turns. In AD&D (1e) you could have used them, at least in theory, because out of combat turns were ten minutes, though we seldom if ever paid attention to that rule. Once the game is in story mode, it doesn't help.