Sometimes you have clues from poetry (and discussions of poetry) or song.
In addition to other comments: sometimes you are lucky, as when someone figured out that Copts speak ancient Egyptian. It was also a semitic language like Arabic.
Of course none of this can be "authoritative" in a substantive sense: not only must Arabic pronunciation have influenced Copt, but you need only look at contemporary time to see how accents etc can vary widely in short geographical distances much less over time. These variations extend to contemporaneous usage of dead languages: I learnt Latin pronunciation in school which apparently is different from usage in the USA, so I can't even make Latin puns with certain people!
So in the end it's just a general idea and a consistent usage so scholars can communicate with each other.
In addition to other comments: sometimes you are lucky, as when someone figured out that Copts speak ancient Egyptian. It was also a semitic language like Arabic.
Of course none of this can be "authoritative" in a substantive sense: not only must Arabic pronunciation have influenced Copt, but you need only look at contemporary time to see how accents etc can vary widely in short geographical distances much less over time. These variations extend to contemporaneous usage of dead languages: I learnt Latin pronunciation in school which apparently is different from usage in the USA, so I can't even make Latin puns with certain people!
So in the end it's just a general idea and a consistent usage so scholars can communicate with each other.