The “proximity rule” you are referring to is that when you have a compound but disjunctive subject, the verb agrees in number with the closer — or in the case of three or more, the closest — of the subjects.
All these are correct, and :
- Either my brother or my sister is going to get it.
- Either my brothers or my sisters are going to get it.
- Either my brother or my sisters are going to get it.
- Either my brothers or my sister is going to get it.
- Either I or my brother is going to get it.
- Either my brother or I am going to get it.
- Either my brother or you are going to get it.
- Either you or my brother is going to get it.
- Either my brother or thou art doomed.
But it is often better to rephrase:
- Either my brother is going to get it, or my sisters are.
- Either my brother is going to get it, or I am.
- Either you are going to get it, or my brother is.
- Either my brother is going to get it, or you are.
- Either my brother is doomed, or thou art.
And then there was nor
This same rule applies (well, or can apply) to neither/nor sets as much as it does for either/or instances. So in all the examples just provided, you can change all instances of either into neither and of or into nor, and the verb remains unchanged. So:
- Neither my brother nor my sister is going to get it.
- Neither my brothers nor my sisters are going to get it.
- Neither my brother nor my sisters are going to get it.
- Neither my brothers nor my sister is going to get it.
All that being said, one can also find examples in writers of renown where neither is used with a plural verb despite both elements being singular themselves.
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