Hello. I have a few of your Gatewoods mixed up in my records, so thought I should reply.
I can only offer my inexpert opinion as to why your John Gatewood was named twice.
First off, there might have been two of your Gatewood's coming in at the same time. Families were certainly moving together. Could be two cousins etc. My family seemed to move in waves back then.
Secondly, and my favorite guess - they made money by importing folks on their patents. Offhand I think they got 50 acres for each name on their list?
So, the incentive was, to import as many as you could. Even if you didn't do it for real. All your named person had to do, was leave the county, then come back in - bingo Import 50 acres! I believe that the importation only meant that your person came form out of county. And you know that the clerk writing all this down with a quill pen wasn't going to check on each entry.
My ancestor, who knows your Gatewoods, patented land in May of 1650 in Essex. Probably imported 3-6 folks himself. However, he -also-, was listed on somebody elses patent in that same month.
So those folks made 50 acres off of having his name listed, even though he was living nearby and had really patented his own land. How could you both patent land, and yet be listed on somebody elses patent?
Game playing to me. They had figured out the system, and good for them.
I know where Button's patent was located - adjacent to where my folks were playing this game (near current Lloyds in Essex Co va). So for what it's worth, that my 2 cents. If you were to force me to prove it, I can come up with a couple names right on nearby patents where my later family members are still playing this game. All late 1600s. I think it was just the way they did business.
Luck with the research. - Mike Merritt