4 Ways to Detect Invisible Yahoo Users
Doodle IMvironment:
Try loading doodle IMvironment. If the user is invisible, it will load. If the user is offline, the message 'Waiting for your friend to load doodle' will appear. But there is a loop-hole to this one because IMvironment can be disabled. But generally people do not disable this feature.

Voice Chat
This might work for the older versions of Yahoo but not 7.0 version. So it's rather redundant now.

"Destealther" Program"
This is a third party program so I am quite skeptical about it. Besides it is troublesome to install a program just for this purpose when it is not foolproof and there are other ways of doing it.

Lastly, the foolproof method (and I thought about it too =P)..

Conference
Invite the user to a conference. If the user is offline, a message will notify you that the user cannot be invited or something like that. If the user is invisible, the invitation will get through. Whether he declines or joins or ignore, it's a dead end. This is a foolproof method because you cannot disable the conference feature. *evil laughter*

Don't worry, I'll try my best not to use any of these methods and no, I am not sick. At least not in the brain. Just minor flu and sore throat =)