I have 4 census records for William and one marriage record.With your birth record this is what I think is happening:
The marriage record says he married Mary Elizabeth Huckaby on 22 Sep 1894.The census for 1900 shows that she is gone...either living with someone else, dead or divorced.It also shows two children:Mayme H., age 2 and John D. age 8 months.
Then, in 1910, there are three more children and a cousin, Jacob L. Brummit age 71. There is a gap between John and the next child of 5-6 years.It also says that William has been married two times and Mary E. has only been married once.The possibilities are that either a child died, it took that long for William to remarry, or Mary had an unusual cycle because there are no further gaps to indicate that Mary might go 5 years without a child.
In 1920, there are 2 more children, and in 1930, a grandson.Mary E. appears in all of them except the 1900 census.
Based on the marriage info in the 1910 census, I think that Mary Elizabeth Huckaby and Mary E. (probably Elizabeth, hence "Lizzie") Brummitt is a second wife.To verify this, I would look for Mary E. Scarbrough in the 1900 census among other neighbors and look for another marriage for both William L. Scarbrough (to a Brummitt).I would also look for a death certificate for the first Mrs. Scarborough between Sep 1899 and June 4 1900.One of those options should work.
The marriage record says: Scarbrough, W. L.Spouse : Huckaby, Elizabeth Marriage date : Sep 22, 1894 County : Anderson Gender : Male Source : County Court Records Microfilm Number : 0979315 - 0979319 genforum.genealogy.com:Anderson Co., TN transcribed marriage licenses ---- The census records are:
1900 Civil District 12, Anderson Co., TN 2nd and 4th June 1900, Sheet 1B, 2A,P 148B, 149A 21 22 Scarborough, William L. Head (not readable on p. 148B) Mamie H. Daug W F Jun 1897 2 S TN TN TN John D. Son W M Sep 1899 8/12 S TN TN TN ---- 1910 Anderson Co., TN 144 145 Scarboro William L. Head M W 42 M2 15 KY KY TN Mary E. wife F W 36M1 15 7 6 TN TN TN Maym H. dau F W 12 S TN KY TN John D. Son M W 10 S TN KY TN Edward Son M W 5 S TN KY TN Laura N. Dau F W 3 S TN KY TN Lissie P. Dau F W 1 2/12 S TN KY TN Brummit, Jacob L. Cousin M W 71 Dv TN KY TN --- 1920 Anderson Co., TN 181 181 Scarborough, William Head M W 52 M MH TN TN TN (overmarked with KY) Laborer Coal Mine Mary E. wife F W 47 M TN TN TN John D. son M W 19 M BWF TN KY TN Laborer Coal Mine Laura dau F W 13 S TN KY TN Sawyer son M W9 S TN KY TN Earl son M W 4 3/12 S TN KY TN ---- 1930 Anderson Co., TN 227 227 Scarbrough William L Head M W 63 M 33 no yes TN TN TNRent 6 Mary E. wife H F W 55 M 25 No - TN TN TN Earl son M W 15 Syes yes TN TN TN Bailey Dowel C. gson M W3 Sno TN TN TN ---