aakk9999 - 8:53 am on Aug 2, 2013 (gmt 0)
The only way I can get these two lines to make sense is if I read each one as meaning the opposite of what I think it was intended to mean sad (I also can't figure out what word your brain was aiming for when your fingers typed "obsolete", but that's minor.)
Are the two bits I've bolded the same thing or different things?
Yes, you are right, the word "obsolete" was the wrong word, replace this with "unnecessary".
There is a request.
The response to this request is 404.
There is some HTML returned together with 404 response, this shows to visitor in the browser.
Having noindex within this HTML is unnecessary. But it will do no harm if included since this HTML that is returned with 404 response is ignored by search engine. And noindex within the HTML returned with 404 response will not speed up removing 404-ed URLs from Google index.
Note that I am not talking about this HTML that is sent alongside 404 as being a separate file somewhere on the server that can be requested on its own right (should someone know the URL for file name) - which would be the only reason for including noindex. From what I gathered, the OP will have to create this HTML that arrives with 404 response dynamically as the "custom 404" that would display to the user would be different depending on business/city.