Your answer reminds me I really should consider the possibility that my Mother's records are wrong (just yesterday I found she had her grandfather's death date off by four years).
There may be cousins to William with the Engert last name, but I have no records of father John's siblings or parents.
But it comes to this: In the 1870 census Father John is age 54, mother Anna is 55, and William is 18. In one of the 1880 census records John is 64, Anna is 63 (we'll let her fudge a bit), and William is 16. We know in this record his age is wrong. It doesn't fit with the 1870 census, the second 1880 census, and the 1910 census.
What was bizarre about this, and what prompted this post was seeing the two records in the same census book only three pages apart.