Well, Abraham Martens Klock is the son of Albert Klock. Albert Klock, so far that I know, was born about 1601 in Holland. I just wasn't sure where in Holland they were from.
And though Tryntie is a southern spelling, that doesn't mean that Abraham Martens Klock was from the south right? Because his wife Tryntie was born in New York. So they could have been from different parts of Holland.
The first link you gave me only goes back as far as 1651 I guess. So I couldn't find anything on Abraham Martens Klock there.
Thank you for the links. I'm going to see if I can find anything in them.