Suppose Jackson and Kim wrote a paper in 2014. When I cite this paper, should it be
Jackson and Kim (2014) show that ...
Jackson and Kim (2014) shows that ...
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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"
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:
If you are writing about the action of the paper, use the singular:
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.