Thank you, Frances. There is no first name but I think it will be "William" Gellin. This likely is the William Gelling who left his quarter interest of Baldel Milne to "his brothers son William Gelling" in 1664. Then in 1683 that William Gelling left "his pte of Baldel Milne" to his [unnamed and underage] "son and heir". That son and heir was John Gelling of Ballamillaghyn of the 1733 will.
I've had to read it over and over to understand it, but I think it's saying it was that transaction in 1655 where William Gellin acquired a quarter interest in the Mill?
A couple of odd things I've collected from past documents puzzle me. One from a long-ago correspondent says that "in 1665 [William Gellin] took over Baldall Mill Braddan from his kinsman William Creer (Junior)".
The other is from an old document I picked up at the Manx Museum in 1976 called "The Gellen Family of Kirk Braddan". It provides a chronology of 5 Gellen family groups. It has many errors and misplaced people, but it has a statement in the "Gellens of Ballamilghyn" page: "1643 William Gellen. He had also Baldwin Mill". So, if this is true, both Ballamillaghn and Baldwin Mill go back farther than I thought. This could be the same William Gellin as the 1655 one. I'm stuck on who his father might be but I estimate William was born 1600 or so.