I'm confused too but I think the way I'd look at is to look fiercely at the 'number' of the subject and stick with wherever that leads you, adjusting both the verb and the complement to match. And in that context the (grammatical) number of 'both' is plural whereas the number of both 'either' and 'neither' are singular. Therefore it would go:

(i) (Both) Don and I are closet people.
(ii) (Both) Don and I are not closet people.
(iii) Neither Don nor I is a closet person.
(iv) Either Don or I is a closet person.

I agree with Tommo that there is something a bit odd about (ii) but I think it is because it is unnecessarily convoluted rather than grammatically wrong. You can't put it right by changing the number. You put it 'right' either by saying (iii) instead, or perhaps by taking the grammatical complexity down a notch by saying something like:

(Both) Don and I are non-closet people.

I think.


 

Well we don't know about Adam, but when according to the Authorised Version Moses asked Him He replied "I AM THAT I AM," adding enigmatically "Thus shalt thou say unto the children of Israel, I AM hath sent me unto you."

However in German it is a different story: He is said to have said "Ich werde seyn der Ich seyn werde" -
something like "I shall be that I shall be."

Later English interpretations we have seen include "I am the one who is," and "I will be what I will be." We are inclined to Believe that He meant to say "I am 'the one who shall be'."

T. S. Gregory, in his introduction to Spinoza's Ethics, takes "I AM THAT I AM" to mean that God exists from the necessity of his own nature, and is His own cause. Vico, in De Antiquissima Italorum Sapientia, says that God is saying that each and every thing is not in comparison with Him.

Here is part of what Schelling in his Philosophy of Mythology says on the question: "That which shall be, is admittedly for that very reason not yet existing, it is, however, not nothing, and so that itself which exists, considered purely as such, is admittedly not yet something existing, but for that very reason not nothing; for it is in fact that which shall be. 'God is that itself which exists' means, according to what has just been said, the same as: 'God in and for Himself, regarded in His pure essence, is merely that which shall be'; and here I again call your attention to how, in the most ancient document in which the true God is mentioned, this God gives himself the name "I shall be"; and here it is very natural that the very same God who, when He speaks in the first person, thus of Himself, calls himself 'Aejaeh,' that is to say 'I shall be,' that this God, when it is a question of Him in the third person, when another speaks of Him, is called 'Jahwo' or 'Jiwaeh,' in short, 'He shall be' . . .

"This ['I shall be the I shall be'] may be translated as 'the I wish to be' - 'I am not that which necessarily exists (in this sense), but am Lord of Existence.' You will see from this how, simply from the fact that God is stated to be that itself which exists, He is also at once characterized as spirit; for spirit is precisely that which can either exist or not, can either express itself or not, which is not obliged to express itself, like the body (which has no choice about filling its space and is obliged to fill it), while I for example, as spirit, am entirely free to express myself or not, to express myself in one way or another, to express one thing and not something else. You will also see, for that very reason, how a philosophy which goes back to that itself which exists and starts out from that, how this philosophy leads immediately, and simply of its own nature, to a system of freedom, and has freed itself from the necessity which weighs down like an evil spirit upon all systems which remain with mere existence and do not raise themselves to that itself which exists, however much they may go on about movement. To go beyond existence, and even to gain a free relationship to it, this is the true endeavour of philosophy. That itself which exists is simply of its own nature also that which is free from existence and in respect to existence, and that itself which exists is all that is important for us. In existence there resides nothing, existence is in every case only an accessory, something being added to that which is."

On a lighter note, Schelling elsewhere and earlier even wrote a little poem about the problem:
           
                        Ich bin der ich war.
                        Ich bin der ich sein werde.
                        Ich war der ich sein werde.
                        Ich werde sein der ich bin.
           
                       (I am the I was.
                        I am the I shall be.
                        I was the I shall be.
                        I shall be the I am.)

Or you could say at a stretch:

                       (I am what I was.
                        I am what I shall be.
                        I was what I shall be.
                        I shall be what I am.)

Logical is not it?

I agree with everything George says here.

'Either/or' and 'neither/nor' constructions both require a singular verb. I'm not 100% sure why 'is' rather than 'am' seemed right to me in my original phrase, but I think the third-person form takes precedence. I'm afraid I can't agree with Richard's idea that the verb agree* with the nearest of two subjects; this would mean you might end up changing the verb if you happened to say 'Neither I nor Don' rather than 'Neither Don nor I'.


*That's a subjunctive, specially for Ollie.

What does this symbol mean to people? --->   

I thought it meant "I am being coy" -- but it seems that it could be interpreted as "I am rolling my eyes in disbelief/pique/annoyance".

I will never use it again. It is too confusing.

I am never coy.

Gosh, you must have a completely different impression of me from the reality.

Probably because 'neither is a closet person' works nicely whereas 'neither am a closet person' doesn't...

What does " " mean this time? You're peeved or you're insinuating something or or or

See what I mean?!

Not that I'm worried about it.