Let’s get the bad news out of the way first — don’t worry, it’s not that bad! Just like other activities that happen on a random basis (e.g., campsite visitors and vendor visits), there’s no set schedule to when you’ll get shooting stars on your island. Well, other than the obvious fact that they occur at night.
On the bright side, anytime there is going to be a meteor shower, Isabelle will let you know during the day’s announcements. So at least you can somewhat plan your day around it! There isn’t anything you can do in the game to ensure a meteor shower — as with so many other aspects of the game, you just have to be patient. Or you can game the system by visiting someone else’s island. After all, you need star fragments, right?