An /anonymous function.

[Galliano]

I would like this. Sometimes you're trying to do your own thing and keep getting friends messaging you to run something, or even just straight up firing party invites at you. If you ignore them you feel bad so it would be nice to remain anonymous from LS, FC, FL and player search from time to time.

[kyuven]

Um, wouldn't your friends message you ANYWAY if they see you're online? Unless you want an invisible option.
Maybe I'm missing something here but isn't this what the BUSY status is for in the first place? If your friends aren't respecting that, you need to talk to them about that.
The only fix is the ability to hide your online status, and that's too easy to abuse. Just because your friends can't see what job you currently are or where you are won't stop them from sending you tells asking you to do things, especially when they can just right click your name and bring up your search info to see what classes you have at what level anyway.
Unless you want /busy to be like /afk in games like EQ1, where it would autoreply with a message of your choosing.