Nelson & His World

I was flicking through a copy of ‘The Naval Chronicle’, when I came across a small account of a pirate laying seige u to the town of Arbroath.
https://books.google.co.uk/books?id=vk4 ... ght&f=true

Finding out the eventual fate of Fall, appealed to my inquisitive nature. I spent a little bit of time surfing the web, but no joy! The few snippets I did manage to turn up related to attacks on shipping around the Great Yarmouth area. The best of which is this link below:
http://www.gtyarmouth.co.uk/Bygones/Aus ... pirate.htm

All snippets I have found simply sign off with the line, that in
April 1782 he was moving into the Irish Sea and that the east coast heard of him no more!
His name also appears a bit of a mystery, he is sometimes referred to as John Fall. Other articles have his name as Daniel and William?
Does anyone have any ideas?