To catch the Legendary Dogs, you do need Lugia or Ho-Oh in your party, but Deoxys isn't necessary. When you arrive in the Trackless Forest, you should receive a message notifying you that your trainer feels the presence of a Pokémon.
The three Pokémon are available during different times of the hour:
- Raikou appears during the first 20 minutes of the hour, from XX:00 – XX:19
- Entai appears during the middle 20 minutes of the hour, from XX:20 – XX:39
- Suicune appears during the last 20 minutes of the hour, from XX:40 – XX:59
Once you catch one, you have to leave the area and come back before another one shows up, which could be one reason why nothing is happening. Each Pokémon can only be caught once per save file.
Another potential issue is if you fainted the Pokémon in battle instead of catching it. In this case, battle the Elite Four and it will become available again.
If a Pokémon still isn't showing up during the time slot it's supposed to, check your system clock to make sure it's accurate.
