Here is an excellent discussion on the use of the reflexive 3rd-person plural when used as 3rd-person gender-neutral pronoun:
Themself or Themselves? (Disponible en anglais seulement)
IntroductionAs discussed in a previous article in Legistics, the plural pronoun “”they”" can be used to represent a singular antecedent that is gender-neutral and indefinite, for example, “”someone”", “”no one”", “”anyone”" or “”a person”". As the article states, the other grammatical forms of the “”singular they”" are “”them”", “”their”" and “”themselves”", and these are used in a sentence to relate to a “”singular they”" subject, along with a plural verb. The question addressed in this article is whether “”themself”" can be used in some cases instead of “”themselves”" with reference to a singular “”they”" or a singular indefinite antecedent.
Recommendations
1. Use themselves as the reflexive/intensive pronoun to refer to an indefinite gender-neutral noun or pronoun that is the subject of the sentence and avoid themself.
2. If a singular indefinite gender-neutral noun is the subject of a sentence, use the “”singular they”" elsewhere in the sentence, especially as the subject of any subordinate clause, to refer to it rather than repeat the noun; this will improve readability. In the following provision, for example, the use of “”they”" as the subject of the subordinate clause, along with a plural verb, instead of “”the person”" and a singular verb, makes themselves sound more natural.
A claim for refugee protection shall be rejected, and a person is not a Convention refugee if they have voluntarily reavailed themselves of the protection of their country of nationality.
3. If themselves sounds awkward, redraft the sentence without using the reflexive/intensive pronoun.
Grammars
According to the rules of grammar, reflexive/intensive pronouns are formed by adding the singular self or the plural selves to the possessive form of the first- and second-person personal pronouns (myself, yourself, ourselves, yourselves), to the objective form of third-person personal pronouns (herself, himself, itself, themselves), and to the impersonal pronoun “”one”" (oneself). Self is chosen if the pronoun to which it is being added is singular, while selves is chosen if the pronoun is plural.

