i copied this from bulbapedia

Every day, a random number between 0 and 65535 is generated by the game. If this number matches the last two bytes of the personality value of any of the Pokémon in the party (that is, the remainder when their personality value is divided by 65536), Mirage Island will appear for that day. The number is generated at 0:00 hours every day and it is active for 24 hours. Even though play time has nothing to do with the real-time clock, a game that has reached the maximum time of play (999 hours and 59 minutes) will not generate Mirage Island numbers anymore.

I remember finding this island when I was young, I never knew it was a secret and I just replanted the Liechi Berry on that island like a dumb :c