Does the word "another" correctly substitute for the indefinite article in this sentence?

I was reading a short story by Ray Bradbury and stumbled on a zero article case in the sentence below.

"Years passed without another visitor, be it boy, girl, tramp or travelling man, knocking at her door."

I feel that this way it sounds good without an article but I cannot explain why it does. 

The form Bradbury uses is informal and one of the few exceptions to the guidance "All singular, countable nouns require an article or other determiner."

It occurs when a list of objects, etc.

(i) is given as general examples, in which case the absence of an article implies "any + singular noun" (as in Bradbury's case)

or

(ii) is repeated in reference to a previous mentioned list, in which case the absence of an article implies "the previously mentioned", e.g. "I was put in charge of the household pets; there was a dog, a cat and a parrot. I left the room for a moment and when I returned, dog, cat, and parrot were chasing each other over all the furniture."

Obviously, it also occurs where

(iii) the noun is uncountable: "Sorrow, joy, and anger were all mixed together."

or

(iv) the noun is the general plural "We see men, women, and children all clamouring for the same opportunities."

Actual examples are hard to find as the nouns vary according to context

The (old-fashioned) 'be it ...' construction is discussed at What does "be it" mean in this passage?

But this allows the use of articles:

• His goodwife will be delighted to have a child, be it a boy or a girl.
• Nell's cooking tonight; we'll enjoy our food, be it the mutton or the veal.

The zero article (but not the identical-'looking' null article) can in certain cases replace the indefinite article, and here adds to the olde-worlde effect.

Be ye man, Be ye wummin,
Be ye gaun, Be ye cumin,
Be ye early, Be ye late,

Dinna furget tae SHUT the GATE.

[Google; Hunters Inn] seems to be a related Scots English example (Be ye [a] man ...).