A specific example from page 341 of America: being the latest, and most accurate description of the New World 1671. I bolded in words where s is replaced by the strange character in the text.
Sir Anthony Shirley
Spanish Dogs
Possession
Five thousand Inhabitants were in a short time reduc’d to less than three hundred, multitudes being put to death in a most inhumane and barbarous manner, …
From what I can gather it seems that if s is left as the letter s when at the end of a word, the second of two-repeating s in a word or in a proper name although this seems more to be when at the beginning of a word in general. I am trying to figure out the syntax used at the time, what this replacement letter for s is called and the history behind it and discontinue use of it.
I am not sure how to even search for this so apologize if it has been asked already.
It's a long-s - a common replacement for an s in English orthography until the 19th century. There was more than one way of writing the 'ess' sound we know only write with 's', after spelling was standardised. As someone who works with early-modern English books a lot I'm not aware that the long-s has any particular significance, but I'm happy to be corrected!
You're asking about the "long S" -- this older post should help.