I’m not sure how they measure how close an accent is. But, they can tell how old accents sounded by looking at songs and poetry for the meter and rhyme of words. If two words rhymed, they were probably pronounced the same way. For example, in Shakespeare’s time they know that “proved” and “loved” rhymed.

well for one from times and places where there was a lot of casual writing there are just straight up people writing about how people speak, which is pretty convenient.

but additionally you can compare different recorded and modern speakers to figure out trends which let you at least vaguely reconstruct what people from the past would probably have sounded like.

and more specifically with new england that’s just wholesale a bunch of people from england who settled a colony, so you effectively have a twin study where you can compare it to modern england.