1850 Keokuk, Iowa Ingle, Wm 49 TN Blacksmith Elizabeth 38 TN Mary 19 TN Matilda 16 TN John H. 14 IN Westley 9 IN (Michael) Anderson 6 IN (Joseph) Louise 3 IN Cass 1-male-Iowa (Louis/Lewis)
1856 Jackson, Keokuk, IA Ingle, William 59 East Tenn - Blacksmith Elizabeth 43 TN Mary 26 TN Matilda 24 TN John 20 IN Michael W. 16 IN Joseph A. 12 IN Louiza J. 9 IN Lewis C. 6 IA
1860 Jackson, Keokuk, IA Engle, J. H. 25 IN Catharin 47 TN Michael W. 19 IN Joseph A. 18 IN Louise 13 IN Lewis C. 11 IA Josephus W. 2 IA
1870 Jackson, Keokuk, IA Ingle, Elizabeth 58 TN J. A. 25 IN Louis 21 IA
William does not appear with the family after the 1856 Census, so I question the 1871 death date--
It appears that they are in Sullivan County, Indiana in the 1840 census.There is a William Ingle in the 1830 Greene Co. TN census.It appears that he is married with a child.If this is your William in Greene, TN 1830, then he was probably married twice.
The original marriage record shows Wm. Ingle marrying Betsy Abel 3/27/1831 in Greene Co. TN.
Not a lot of help, but maybe you can come across something by following the kids.