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Suppose Jackson and Kim wrote a paper in 2014. When I cite this paper, should it be

Jackson and Kim (2014) show that ...

or

Jackson and Kim (2014) shows that ...

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    I am not sure enough about a general rule to write an answer, but to me, the construction "Jackson and Kim (2014) shows that ..." looks equivalent to considering the citation reference a word in the sentence in other citation styles such as "[1] shows that ..." or "[JK14] shows that ...", which I have seen criticized as bad style in reviews.
    – O. R. Mapper
    Commented Jan 17, 2015 at 14:12

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This is a special case of a more general problem about 'plural' names for specific organisations/groups, which often comes up (and is different in the UK and US, to complicate things) - for example, https://english.stackexchange.com/questions/138238/are-vs-is-for-proper-nouns-which-sound-plural-such-as-band-names

Generally speaking, either is legitimate - it depends in part whether you think of "Jackson and Kim" as the name of a single entity, the paper, or as referring to two individual researchers who happen to be mentioned together. You can also avoid this entirely by using the past tense - "Jackson and Kim (2014) showed that..." is the same whether you think of J&K as one entity or two. (Ditto for "found", "proved", "refuted", etc). This would be my personal preference.

Ultimately, though, all questions of style in academic writing can be answered with "have a look at what other papers in the field use; if you're thinking about a specific journal, have a look at what's common there." If they all use "show" for multiple authors, you probably want to use "show"

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As a matter of basic writing style, this comes down to whether you intend the authors, or the paper, to be the actor in your sentence.

If you are writing about the actions of the authors, you should use the plural:

  • Watson and Crick (1953) use only two pages to describe the structure of DNA.

If you are writing about the action of the paper, use the singular:

  • Watson and Crick (1953) serves as an example of how a breakthrough paper can launch its authors to academic stardom.

Usually the issue is not so clear cut, because usually we are simply describing the results from the paper rather talking explicitly about its authors or about it as a document. In this most common case, the usual convention is to treat the authors, not the paper, as the actors and thus use the plural.

  • Watson and Crick (1953) demonstrate the double-helical structure of DNA.
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