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Consider the following sentence:

We assume that the individual(s) possesses some general knowledge of the rules of football.

Is "possesses" correct there? Should it be "possess"? Is the rule more complex than always using one or the other?

There are at least two references that say the verb should be singular.

"... when an 's' or 'es' is added in parentheses to a subject or subjects, the verb should be singular because the 's' or 'es' is parenthetical. [For example,] The name(s) of the editor(s) of the book in reference 2 is unknown." APStyleManual

"When -s or -es is added parenthetically to a word to express the possibility of a plural, the verb should be singular. ..." AMAManualOfStyle

I have seen none that say the verb should be plural.

It is merely customary, in sentences involving parentheses, to write them so that even if everything within parentheses is ignored, the sentence is still readable and the meaning does not change much. In this case, dropping the "(s)" would result in "individual", so "possesses" has been used accordingly.

Actually, to adhere perfectly to the convention (so that the text is readable even if no parentheses are ignored), one may instead write

We assume that the individual(s) possess(es) some general knowledge of the rules of football.

so that the sentence can be read either with both parenthetical parts dropped or with both included, and remain grammatical. But including too many parentheses is considered poor style, as the result is usually awkward to read. Also, unlike this sentence, it's not always possible to satisfy both "branches" (of whether the part within parentheses is read or not), so some compromise is often inevitable anyway — and the choice that is often made is to be consistent with the text without the parentheses (or else whichever option is more likely, depending on the writer).

I think you can do either, really. I would slightly prefer to agree with the plural, and so write "possess" in your example. If the sentence is read out loud, it sounds like the plural is in operation, so having the verbs be singular is then awkward. But I suspect there are cases where the singular would feel more natural, and it seems equally acceptable to go with that.

When I am writing such a sentence, I make them match the parenthetical plurals wherever they occur, if possible:

We assume that the individual(s) possess(es) some general knowledge of the rules of football.

This is not always possible, and in those cases I prefer to recast the sentence. :)

I try to avoid optional plurals, and instead use the plural form, as the specific case of only one of the objects in question is covered by the general case of multiple objects.

In my opinion, treating optional plurals is the same as treating compound subject joined by the word or (having choices as implied by the word option). Reading the given sentence should go like this:

We assume that the individual or individuals _______ some general knowledge of the rules of football.

What verb form must be used to agree with the compound subject?
As a rule, if the individual parts of the compound subject are joined by or or nor, the verb form which will agree with the subject closer to the verb must be used.

Therefore in this case, the verb form to be used should be possess instead of possesses since the subject closer to the verb is plural.