This is my working hypothesis - the way I see it as of this moment!!  
based on research by J Roy Parker Jr and his cousins

". .our Elisha Parker, whose residence in Hertford County always seems to have been on what is now the road from Ahoskie to Harrellsville, early known as Pitch Landing or Bethlehem Road. Elisha married Penelope Dilday born in 1795. She was still alive when he wrote his will in 1868." ~ Roy Parker

 "Elisha b. 1787 became 21 in 1808 and he shows up on the Gates Tax Lists in 1810,  Abraham Cross's captaincy, (p. 61) with only a poll-tax, and that was it.  He drops out of the Gates County records that I have on hand, so probably went to Hertford ca. 1811." ~ Ray Fouts

   "In 1861 Elisha Parker deeds his farm to his son Joseph Benjamin Parker. Hertford Co Bk A-228 Dec 1868. Deed made 10 Sept 1861. probate 7 Dec 1868.
Elisha Parker to Joseph Benjamin[son] 121 acres for $120 including two grants of 100 acres obtained by Elisha in Nov 1834, 71 acres in Nov 1835.  Elisha and present wife Penny keeping for life. . .on White Oak Swamp, adjoining Lawrence Askew, Ely Willoughby and others. "These were 'grants' because the Hertford County courthouse burned in 1831, and landowners who already had property were given special 'grants' of the property they already owned. This property lies in the eastern side of the present-day Harrellsville Road and Newsome Grove Road. White Oak Swamp runs east-west just north of Harrellsville Road. It rises on the east side of the town of Ahoskie and flows into Ahoskie Swamp." ~ Roy Parker

Children of Elisha Parker and Penelope Dilday:
1. ?James [Jim] Parker  went to Texas also
2. William Dossie Parker 20 Feb 1827 - 23 Feb 1859 Texas of diptheria
           east side of Brazos
      married in TX 15 Jan 1856 Susannah Parthenia Autry ca 1836 - [issue]
3. Blake Parker   1830 - 1868
4. Martha Parker  ca 1830 -
5. Emma Parker  1832 - ca 1866 San Antonio TX  [issue]
      married Jesse Brown 4 May 1819 -
6. John Brice Parker 23 Sept 1835 - 24 Oct 1921 Dallas Co TX
      married Martha Ann Barnes  [9children]
      a. Alice Amanda Parker
      b. William D Parker
      c. Ruzela Parker
      d. James W Parker
      e. Eller W Parker
       f. Elisha J Parker
     married 2nd Mary Maglene  [9 children]
7. Joseph Benjamin Parker 1837 - 1871
      married Sarah [Sallie] Askew 1834 - 1915 ts
       a. Rosa Lee Parker 1858 -
       b. Mary [Mollie] C Parker 1859 -
       c. Ann Eliza [Anna] Parker 1863 -
       d. A-athusa [Toocy] Parker f 1864 -
       e. David McN Parker 1866 - 1886 ts
       f.  James D Parker   1867 - 1895 ts
       g. Joseph Thomas Parker 1870 - 1933
                  listed as Elisha F in 1870 census

    "My husband's family are also Parkers from Hertford/Gates/Bertie Counties.
There were just so many Parker families in that area and many with the same
names. We have only gotten back to Elisha Parker b. about 1787 in Gates
County, NC. (according to census records) and died about 1868-1869 who
married Penelope Dilday. They are both buried in the Parker Cemetery on
Harrellsville Road outside of Ahoskie on land which is still in the Joseph
Benjamin Parker family. My husband's grandfather, John Brice Parker (brother
of Joseph Benjamin),  came to Texas in about 1883-1884 with his first family
(wife & 9 children) and settled in the Dallas area where his first wife,
Martha Ann Barnes died. Then he married his second wife and proceeded to have
9 more children (my husband's father is from the second batch).
I might add that he also outlived his younger second wife and died at the age
of 86." ~ RaNell Parker

1812 NC in the War of 1812 - Published Reg
1st Regiment - 6th Company Detached from Chowan County Regiment
 Elisha Parker . . .Number 55 or 57.

"The Elisha Parker from the War of 1812 was yet another Elisha, related to yet another Peter Parker.  You know they stayed up nights, trying to drive us nuts!  There were also two men named James who had sons named Amos. Why not?" ~ Ray Fouts

1815 An Elisha Parker appears on tax roll in Edwad A Callum's Dist. . .1 free poll
 also, Isaac Parker - 475 ac .. two polls in household... $948
    also, Luke, James and John . . all single free polls

1832 In the estate of Elisha Lawrence, there is a $13.75 bill owed to Elisha Parker.
Elisha Parker bought a bushel of peas in the Larence estate.
In the estate of George Dunn, Dunn owes Elisha $2825 [These Elisha ref are to the Elisha who lived in the Northern Distr over in Murfreesboro]

In 1859 Elisha is witness to will of John Rasberry. . who leaves to two sisters, including Mourning Rasberry, land near Stony Creek. . Mourning's will in 1868 includes land on White Oak Swamp.

1830 US Census Southern District Hertford County
 Elisha Parker  2m 5-10; 1m 40-50; 2f 0-5; 1f 30-40 

1850 US Census Southern District Hertford County
 160/160 Elisha Parker       63 cooper
               Penelope Parker    55
               Joseph B                  13
               John B                      15
               Martha Parker       20

1860 USCensus Southern District Hertford County
591-649 Elisha Parker        75 farmer    Gates Co
                 Penny Parker        66                 Hertford Co
                 Martha Parker      25                     "

Elisha Parker d 1794 |  his parents
& Rebecca Warren |  her parents
of Gates County NC

 - Will of Elisha Parker - Gates Co - 26 July 1793 - prob Feb Ct 1794
- wife Esther - son Peter, daughters Elizabeth Eason and Mary Griffin, sons John and Jesse, daughter Peggy Parker, son Elisha, daughters Christian and Nancy, grandson John Griffin, 
- wife Esther, sons John and Elisha Exrs. 
Test: John Parker, Daniel Parker, Pa Haggerty. NCHGR 2-63

Children of Elisha Parker d 1793/94:
1. Peter Parker
2. Elizabeth Parker
     married Eason
3. Mary Parker
     married Griffin
      a. John Griffin
4. John Parker 
John received no land in the 1793 will, so was probably the eldest."~Ray Fouts
5. Jesse Parker d 1800
      married  Charity Cross 
              dau of Hardy Cross d 1816
       a. Hardy D. Parker
       b. Joseph Parker  dy?
             who doesn't seem to have survived.
6. Peggy Parker
7. Elisha Parker d 1806
     married 18 Aug 1800 Peggy Lee
      a. Elizabeth Pipkin Parker
      b. Polly Lee Parker
8. Christian Parker
9. Nancy Parker

Peter Parker d. 1778  |  his parents
of Gates Co NC