Hi. If your 2nd great-grandfather is William Taylor 1843-1921 then we are fourth cousins. John Wade Taylor was my 2nd great-grandfather. He emigrated from Northumberland to Utah in 1863. John's son, William Taylor, is my great-grandfather. William's youngest son, Vernon Taylor, was my grandfather.
One of your 2nd great-grandfather's sons, Matthew Taylor 1869-1955, emigrated to Australia. He had 7 daughters. I have contact with a couple of our other cousins who live there. One of them sent me a couple pictures of William Taylor with two of his sisters, Jane and Rachel. I have attached them.
I am willing to colaborate and answer questions. I sent you a private message with my email address.
Kind regards, Merrie Richards