How can it be decided whether two grammatical cases should be taken to be just homophonous (i.e. as separate) or actually equal?

Question

I've come across this in multiple grammars: Two grammatical cases (e.g. ergative and instrumental) are said to be "homophonous" - they make use of the (apparently?) same marker and yet, they are annotated differently in the examples. What are the factors through which can be decided whether those cases are justifiably labelled distinctly or if I should view them as one, regarding the "difference" between the two simply as "additional semantic information"?

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Here are two examples for the ergative/instrumental distinction that I had at hand, there are probably better ones:

In the grammar for Ese Ejja (ese, Vuillermet 2012), the author repeatedly mentions the "homophonous instrumental" (p. 197):

When the ergative (or homophonous instrumental) case is associated with nouns, then only (gliding) transitional sounds is occasionally heard with the front vowels i and e and with the back vowel o – cf. the missionary transcription for Ernesto + =a .

In the Bantawa grammar (bap, Doornenbal 2009), "instrumental" is merely called a "role" that ergative might take (i.e. a possible translation, p.75):

The ergative may also be affixed to nominals in roles that would usually be called ‘instrumental’. Noun phrases that are marked with the ergative but do not act as the agent in a verb frame translate as instrumental modifiers. There is no separate instrumental case, however. Ergative-marked instrumental phrases are adverbial modifiers denoting either the cause, the method or the instrument of the action.

Answer 1

The conclusion that "lam" (take it on the lam) and "lamb" are homophonous is justified by the fact that the words are pronounced the same but have different semantic or syntactic properties. But syn-sem sameness / difference can't be measured in a vacuum. So one might then conclude that the nominal suffix -s in "I have 4 cats" is a "plural" suffix and in "I hate cats" it's a homophonous "generic" suffix. However, there are perfectly reasonable theories of semantics that allow you to simply say that these instantiate a "plural" suffix, where one semantic property covers both uses. In this case, it turns out that there are a lot of ways of forming the plural, and you don't find "the generic" being formed one way while "the plural" is formed a different way. If you did, you'd have a clear argument for saying that in some cases the two functions are homophonous in certain cases.

Authors may adopt theoretical frameworks that could dictate for example that if semantic functions A and B can be marked distinctively in some language, then that fine-grained distinction is covertly present in all languages. I haven't ever seen anyone say that overtly, but some such thinking may underly the claim of homophony. In the case of "ergative" vs. "instrumental" (at least if you treat "ergative" as a fundamental case relation and not simply the result of obligatory passivization), the semantic and syntactic contexts for selection of one affix vs. the other are disparate enough that distinct descriptions of distribution would be necessary, which then would mean that these are homophonous morphemes.