It is a very unusual use of neither where it ought to be "... use it to say ‘not either’ in relation to two things."
But it does have a ring to it and fits in with the plethora of idioms in language today that are ironic, (not many though & even then the continued usage is usually oblivious), or based on mishearing or misunderstanding.
The "double negative" aspect of it works.
There are some phrasing things that struck me but that's me not your writing.
Nice uncomplicated arrangement and mix.
Well done B.D.

Cheers
rayc
"What's so funny about peace, love & understanding?" - N.Lowe