I am thrilled for you, as this does appear to be your John L. Lindsey's family. It seems that Sylvareus was likely meant to be Sylvester, but either Caleb was unable to pronounce the name correctly because he was so near death, or the person who wrote what Caleb said did not know how to spell Sylvester.
So now it seems that John L. Lindsey was living in Wilson County in 1815.Ancestry.com has tax lists for Wilson County for 1803-1807, and a John Lindsey appeared each year from 1804-1807.Maybe this is your guy.
I would like to have a scanned copy of the will, if it is not too much trouble.Even though John L. Lindsey was not part of my group of Lindsey's, I have spent a lot of time studying him because of William Lindsey McDonald's book, which placed John as a son of "my" Samuel Lindsey.We now know that McDonald was incorrect about John L. Lindsey's ancestors.
John L. Lindsey stated in the Rev. War penison application of John Copeland that he had known Copeland when he was a soldier. This statement places John L. Lindsey near John Copeland during the war.Copeland stated that he had enlisted in Chatham County, North Carolina.So it seems that John L. Lindsey lived in or near Chatham County during the Rev. War.And the Chatham/Orange County area is where we see other Lindsey's using the naming pattern of John>Caleb>John, etc.
I think the will is another piece of evidence for you that places your John L. Lindsey as part of the Chatham/Orange County Lindsey bunch, some of whom migrated to Maury County, Tennessee, where your John and his son, Sylvester, appeared on the census in 1820.
Now it appears that John L. Lindsey spent some time in Wilson County before moving on to Maury County.