How do you make mirage island visible?

It only appears when it wants to,you never know when it will appear.

It's completely random.

Well it depends on what Pokemon you have on your team at the time, because each Pokemon has a sort of number like the trainer ID but Pokemon style you can't find out what this number is it's built into the game and the island goes by that number when it appears but it's a random number every day so just try every Pokemon in your team and in your box until it appears, but if you don't want to do that I supose you could just wait until it appears by itself.

Every day talk to the guy in the house It happens randomly.

Is there an action replaycode?

Go to Pacifidlog Town, you need surf to get there. Or ou can fly of you have already visited it. From the Pokemon Center go down then take a right, keep walking right until you can only go up. If you did this right you should enter a hut with to elderly men. One is a Gentlemen sitting at a table, he just talks about Mirage Island. The other one is looking out a window, or so it appears. Talk to him, he will either say, "I have not seen MIRAGE ISLAND today." or, "I have seen MIRAGE ISLAND today." If he said he's seen it travel surf off Pacificdlog in the direction the man was facing. It will take some searching, but you should eventually find it.

If he said otherwise, save your game, turn off the DS, then go to the time and date menu and set the date a day ahead. Then let it save and turn off the DS again. Fire up Pokemon and then go to the Pokemon Center, go to your box and deposit all of your Pokemon, then withdraw 6 new ones. If you are in Pacificdlog town already go back to the old man's house and talk to him again. If he says he still cannot see it repeat the process. With luck and several different Pokemon it should appear at some point.

When you finally get to visit the island bring lots of Pokeballs becaus you can catch wynaut there. Also the rare leichi berry is there for the taking. THERE IS ONLY ONE IN THE ENTIRE GAME so be sure to plant it, grow it, pick, and plant it again to have never ending leichi berries!

Hope I help and you can only access Mirage Island AFTER you beat the Elite Four! *Sorry if there are typos*

"Mirage Island will appear on Route 130 if the 2 bytes from the Mirage Island value in reversed order match the last
2 bytes of the PID from one of the Pokemon in the players party.
The value changes everytime a day passes by. This means if the battery had run dry the value won't change anymore.
It is even possible to visit the island when you already started your game with dry battery. In that case the value will
Always be 00 00

Mirage Island value location in save file
The save file is splitted into 2 save blocks (and a third unimportant/unknown block).
Each save block is again splitted into 14 sections (IDs 00 - 0D) with 1000 bytes each.
The section ID is located at the end of each section at offset 0xYFF4. Y can be any value from 0 to D.
To find the right section just replace Y with any of those values and look for the byte 02.

The Mirage Island Value are 2 bytes that are located in the section 02 at the following offsets:
Ruby & Sapphire0xY408 - 0xY409
Emerald0xY464 - 0xY465

Example (Ruby/Sapphire):
At 0x2FF4 I have found the section ID 02, so I had to look at 0x2408 for my value.
The 2 bytes at 0x2408 in my save are 86 B0.
That means the PID from one of the Pokemon in my party converted to hex should match XX XX B0 86.

Knowing this it is also possible to create a Pokemon with the required PID.
I took that two bytes from 0x2408 in reversed order, added two random bytes at the beginning (e.g. D5 62 B0 86)
And converted it to decimal to get 3580014726.
Then I used A-Save to change the PID from one of my Pokemon to 3580014726 and Mirage Island appeared!"

Source: https://projectpokemon.org/forums/archive/index.php/t-44242.html