Defining the vocative: something like "a form used for address"
I didn't give a definition of "vocative" in my original question, but it seems like it might be worthwhile, since there are a few constructions that look similar that we might want to distinguish.
It seems necessary to start with non-neuter -us nouns of the second declension like "Brutus" and "Marcus", because they are the only category of nouns (if we set aside borrowed nouns) that show a distinct form for what is called the "vocative case". So for an initial definition, we could say that in the context of Latin, "vocative" refers to a form that is used in the contexts where forms like "Brute" and "Marce" would be used.
What remains is to determine in which contexts forms like "Brute" and "Marce" are used.
Although I don't have a full understanding of this, Ashdowne (2002) indicates that the factor connecting the different contexts in which the vocative case is used is the function of address. Alex B.'s answer to How do you address someone in a case other than the vocative?, which cites Pinkster 2016, also indicates that there is a connection between forms of address and the vocative (Alex B.: "forms of address are always in the vocative").
The particle O can be used with addresses, but also with exclamations, so its use doesn't seem to be a completely reliable diagnostic of the vocative case for neuter nouns. Ashdowne mentions O and says "it is reasonable to assume that a form which could be either nominative or vocative is in fact vocative when accompanied by o!" (p. 144) but also says in a footnote that "A neuter noun in such circumstances could also be accusative and accordingly could be a thing exclaimed over" (p. 145). I think that "o tempora, o mores" in the passage quoted in fdb's answer refers to "a thing exclaimed over" rather than acting as an address, and for this reason, I don't think it is a true example of a neuter noun in the vocative case.
At least one example of a neuter vocative does seem to exist
Bennett (1914) seems to have a long list of examples of the vocative. One in particular that seems to fit is limen in Plautus's Mercator 830 (Bennett p. 268). Bungard (2008) provides the following translation of the sentence with limen:
Limen superum inferumque, salve, simul autem vale. (830)
Doorway above and below, hello and at the same time moreover farewell.
This is certainly an unusual situation, but it seems to be a quite literal case of addressing an inanimate object, so I think there is no reason to interpret the phrase at the start of the sentence as anything other than a vocative.
Other possible examples
Ashdowne (2002) mentions another possible example. O Pergamum occurs in a list of vocative phrases that includes the unambiguous form "Priame":
5) o Troia, o patria, o Pergamum, o Priame ... senex (Plaut. Bacch. 933)
O Troy! O fatherland! O Pergamum! O old man, Priam!
However, in a comment, Unbrutal_Russian suggested that it's not actually totally clear that the successive nouns preceded by "O" here all have the same function.
Whether or not this is actually a solid example, it seems plausible to me that a city name might be used in the vocative to address a city as a whole, and there are a number of cities or towns with neuter-gender names, so this seems like a situation where a neuter vocative might be used. The following quotation is not Classical Latin and doesn't involve a neuter noun, but it does seem to be an unambiguous example of a city name being put into the vocative case:
Et erit in die illa: in oblivione eris, o Tyre! septuaginta annis, sicut dies regis unius; post septuaginta autem annos erit Tyro quasi canticum meretricis
(Isaias 23:15, Vulgata)
Terms of endearment
A class of words that I had forgotten about when I posted my original question is neuter nouns used as terms of endearment, like mel.
In the section on "Expressions of Endearment", Bennett mentions meum cor, meum corculum, mel meum, meum savium, meum labellum (p. 273). But I'm not sure that this use characteristically requires a "vocative case" form since there are some masculine examples in the same section that look like nominatives: meus ocellus, meus molliculus caseus.
Maybe looking at the exact context would make the situation more certain: the answer by Alex B. that I linked to above indicates that the nominative case is used for appositive expressions specifically.
Ashdowne, Richard. "The vocative’s calling? The syntax of address in Latin". Oxford University Working Papers in Linguistics, Philology & Phonetics, Volume 7, May 2002, pp. 143-162.
Bennett, Charles Edwin. 1914. Syntax of Early Latin: Vol II—The Cases
Bungard, Christopher William. 2008. "Playing with your role in Plautine Theater"