grammaticality - Why is 'neither' (without 'nor') singular?

I ask about 'neither' as a determiner. I want to dredge below the last 5 paras under 'Tip 2' , which don't explain. Neither does p 90, A Student's Introduction to English Grammar (2005).

Consider: 2. Neither of the parties ?IS? concerned.
= 3. Both two or more parties are NOT concerned
Does the plurality of the verb in 3, prove that 'neither' should be plural? Why or why not?

I edited the nouns in the original below to simplify.

You need to be careful, because there are two separate situations.
[I omit the second situation here, which I ask NOT about.]

(1) "Neither" withOUT "nor", as in "Neither of the ... parties is concerned with Egypt."

If it is "neither" only, then it is singular and takes a singular verb even though the plural verb might sound better to us.