There are two factors to consider when determining whether the tab is displayed:
- The parent menu item
- The result of the access callback
You probably cannot do much about the parent menu item, because this points to the generic
You can, however, influence the result of the access callback by configuring how to validate the argument. This allows you for example to display the tab only for nodes of a certain content type. Of course you will have to configure the view to hide the view/display 404 if the argument does not validate.
A fancier validation would be possible if the validation configuration dialog would allow you to enter PHP code. I don't know if this is the case, so you might have to look for a different solution.