I'll explain my example further:
'either...or' and 'neither...nor' are distinguishing between two (only) choices. Those choices could be the subject, the object or even the verb of a sentence.
If you position 'neither' (or 'either') before the subject, then the other choice will be another subject, not a verb or an object. This is the case in your first example: 'neither you nor I...'.
The same happens with the verb: "You must either eat or drink something today".
And with the object (indirect or direct): "I'll give this present to either Rob or Lucy, it doesn't matter which one receives it." "I'll give either this present or that one to Rob. It doesn't matter which one he receives."
So the deliberate mistake in my earlier post is that I put 'neither' before the verb, but 'or' before the object. Well done with your corrected version, which shows that you worked this out. There is a simpler alternative, however: "You can have neither chocolate nor ice-cream until tomorrow." which avoids repeating the subject and verb.
To answer your other question: with more than two items, there are several possibilities. Remembering that we are still choosing only one item, we could say:
In the positive: "I can choose the course I want to do - physics, chemistry, computers or maths."
In the negative: "I couldn't see, hear, smell or speak after my accident."
In those examples I just put a comma after every item until 'or' (with no comma) before the last one.
Another option is to use 'any', 'any one' or 'none' and leave out the list of items. So:
"If I had to choose any one of those subjects, it would be maths."
"None of the corners of a square can be more than 90 degrees."
Final note: because 'either' and 'neither' are a choice that allows you to pick just one of two items, the verb must be singular. Don't say "neither of them are handsome", although I'm sorry to say that many English speakers do. :shock:
So can you now tell me how to express my earlier thought about the weather tomorrow (raining - snowing - sleeting)?
I'll let fivejedjon tell you more about his examples of another use of 'either' and 'neither'.