I found a picture of Joseph Thomas & a monument. Here it isA google search on "white pilgrim" turns up a lot of white pilgrim clothes. I did find This site. It gives the full poem as written by John Ellis, but the first verses as written in 1836 at the grave & the later verses beginning with the 'I called at the house' line, called "REPLY TO WHITE PILGRIM" Written at Yellow Springs, O., 1843.
Thomas died & was buried in New Jersey. I think Antioch College is in Yellow Springs, so if Thomas' family lived there, it would make sense for Ellis to write an addendum after a visit there.
Jean, I also found that you recorded it on "Sweet Rivers."