"Should either be" or "should be either"?

Solution 1:

It's fine either way. I parse your first example as:

...should be [either [visible] or [invisible]]...

That is, what an object should be is either "visible" or "invisible"; and the second example as:

...should [either [be visible] or [be invisible]]...

Meaning that what an object should do is either "be visible" or "be invisible".

In this syntax, the repeated verb (here be) can be omitted because it's clear from context, however if you have multiple items with mixed verbs, then the verb is required for every item.

Solution 2:

I would not consider either sentence unusual in form.

The verb phrase should be can be quite acceptably split. (Unlike the more controversial issue of infinitives.) Hence, both forms are grammatically acceptable.

To me, the former is slightly more natural (when speaking), while the latter is essential when you want to use two different verbs in your "either ... or ..." phrase.