Hey pawnswizard,
the VisibleIf-function is simply a description about the visibility of a node or a parameter.
It is driven by the values (inputs) of parameters, this is why you'll need to start with 'input["name"]'.
You can't make primary inputs visible based on other primary inputs, unfortunately. The 'input' just works with Integer, Float and Boolean values. What you can do, though, is to create a Drop-Down list or something else that will let you choose how many primary inputs you want (like in the multi switch nodes)
Hope that helps
Best Regards