I don't believe anyone knows for certain precisely where any of the children were born.  The locations given by secondary sources appear to be deductions based on the presumed location of the parents, which is fine, provided you really know where the parents were.  As the timeline below shows, we have only a few primary records proving where the parents were located.  Most of the birthdates are equally unfirm.  However, the move from Kendricks Ck. to Pendleton Dist. to Christian Co. does follow the same track as Benjamin's father and other family members, so I do not doubt those locations.

• The Tradewater River flows NW from central Christian Co. to form the boundary between Hopkins and Caldwell Cos.  Apparently, Benjamin and Patience lived on the southwestern (Caldwell Co.) side of the river.
• The name of the Town of Elizabeth was changed to Hopkinsville in 1804.
• Benjamin's brother, John, was the County Clerk of Christian Co., which may explain why several of his children got their marriage licenses there, instead of at the county seat of the county in which they were living (viz., Livingston Co. or, later, Caldwell Co.).

1.  Family Group Sheets compiled by Georgie Tolleson and Betty Ann (Matthiesen) Cogliati, citing:

Letter of 1842 in possession of Georgie Tolleson Will of Henry CLARK Sr. Christian Co. KY Will Book C pp 516 Christian Co. KY Marriages Caldwell Co. KY Marriages Cole Co. MO US Census 1830-40-50-60-70 Osage Co. MO US Census 1850 Gibson Co. Ind. Marriage Book A, #14

2.  Will of Col. Henry Clark in which he makes a bequest to Hester (CLARK) FINLEY, daughter of his deceased son, Benjamin — the only one of Benjamin's children who was still living in Christian Co. at the time Henry wrote his will. 

3.  Census Index:  U.S. Selected Counties, 1790 (Broderbund CD-311):

1790

Clark, Capt. Benjamin

SC

Pendleton Dist. [now Anderson Co.]

p. 83

1-3-3-0-0

These data indicate:

Gender and Type	Age Class	Therefore Born	Individuals Inferred
1 free white male	16 and over	in or before 1774	= Benjamin (b. ca. 1759)
3 free white males	15 and under	1774-1790	= Isaac (b. 1783) = Vachel (b. 1784/5) = Henry (b. 1785/6)
3 free white females	all ages	in or before 1790	= Patience = Hester = Sarah

For neighbors, see 1790 Census Table. 

4.  1800 Census.  1800 KY Census lost/destroyed.

5a.  Census Index:  U.S. Selected Counties, 1810 (Broderbund CD-313).  Please see my WARNING regarding use of this database (the numerical data has the genders switched). 

1810

Clark, Patience

KY

Caldwell Co.

p. 5

11010-2031007

5b.  1790-1870 Census Index (online at Ancestry.com):

1810

CLARK

PATIENCE

KY

Caldwell Co.

p. 5

20310-11010-07

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
2 males	9 or under	1800-1810	= Ephraim (b. 1803/4) = Louis? (b. ca. 1800) or Michael?
3 males	16-25	1784-1794	= John (b. 1790-1800) = Benjamin (b. ca. 1792) = Henry (b. ca. 1785/6)
1 male	26-44	1765-1784	= Vachel (b. 1784/5) = Isaac (b. 1783)
1 female	9 or under	1800-1810	= Susan (b. 1801)
1 female	10-15	1794-1800	= Sarah
1 female	26-44	1765-1784	= Patience (b. ca. 1763)
7 slaves	all ages	in or bef. 1810	= names unknown

Patience may be fibbing about her age or 1765 may be closer to the truth.  Where is Michael?  Has Louis died and do we have the wrong birthyear for Michael?

6.  1820 Census.  Patience appears to have gone to Missouri.  Missouri did not achieve statehood until 1821, so there was no 1820 Federal Census of Missouri.  Patience passed away before the 1830 Census.

7.  Family Quest Archives:  Missouri Federal Census 1830.  Heritage Quest CD M19-72.

1830

MO

Cole Co.

p. 187A

Ephram Clark

001 010 - 000 000 001

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	10-14	1815-1820	= Ephraim's son?
1 male	20-29	1800-1810	= Ephraim (b. 1803/4)
1 female	60-69	1760-1770	= Patience (b. ca. 1763)

The female appears to be Ephraim's mother, Patience.  Ephraim appears to be a widower and the boy his son.

8.  Anon.  1990.  Logan County, Kentucky, Taxpayers, 1792-1799.  T.L.C. Genealogy, Miami Beach, FL.

1792-95 Tax Lists	[not found]	KY	Logan Co.
1796 Tax List	Clark, Benjamin	KY	Logan Co.
1797-99 Tax Lists	[not found]	KY	Logan Co.

I think we can confidently place Benjamin's arrival at 1995-6.  As expected, he drops off the Logan Co. tax roll when Christian Co. is formed in 1797.  (Also on the rolls in 1796 only are Jesse CLARK (his first cousin?), Isaac DAVIS (his brother-in-law), and William FRENCH (his brother-in-law). 

9.  Census Index:  U.S. Selected Counties, 1800 (Broderbund CD-312):

1800 Tax List

Clark, Benjamin

KY

Christian Co.

10.  A.B. Willhite.  [n.d.]  Christian Co., Kentucky, Tax List, 1804-1809.  (self-published; available from author at 4396 Coopertown Rd., Russellville, KY 42276, or from the Christian County Genealogical Society, Hopkinsville, KY):  Benjamin Clark not found, which seems to mean he moved to Livingston [now Caldwell] Co. before he died.  The Livingston Co. tax rolls should be examined.

11a.  Lon Arneld Bostick, Sr. & James Taylor Killebrew.  1985.  County Court Order Book "A" for Christian County, Kentucky for the Years 21 March 1797 - 29 August 1805...  Christian County Genealogical Society (1101 Bethel St., Hopkinsville, KY 42240).  First column is the page number in Bostick & Killebrew; second column is the page number in Court Order Book A.  "WB" Numbers are entries that somehow ended up at the back of Will Book B.  "A" numbers are a set of pages at the beginning of Order Book A that were separately numbered and indexed.

p.	p.	Date	Motions
12	WB-29	27 Mar 1798	The Court proceeded to the Election of a Clerk and John Clark having produced a certificate from the Judges of the Supreme Court in the following words (to wit) State of Kentucky, We do hereby certify that John Clark hath been examined by our Clerk in our presents and under our direction and that we judge him to be well qualified to execute the office of Clerk of any County Court or Court of Quarter Sessions within this State.  Given under our hands and seals as Judges of the Court of Appeals this 27th day of March 1798.  ATTEST:  George Muter; Caleb Wallace; Thomas Todd, C.C.A.
13			And on examining the ballots found a majority in favor of John Clark.  It is therefore ordered that he be permanently appointed Clerk as the Justices present having all concurred.  He having entered into bond with Benjamin Clark his security in the penal sum of
	WB-30		one thousand pounds conditioned as the law directs and took the oath prescribed by Law and the oath prescribed by the Constitution.
21	27-A	16 Oct 1798	On motion of Wm. Hynes ordered that Benjamin Clark, Vachel Dillingham, Abn. Stuart, Nicholas Lockerman, Wm. Gillihan, and Robert Cravens be appointed Commissioners to divide the land between Jno. Handley, Richard Jones Waters, and Jno. Gater.
22	29-A		On motion of Benjamin Clark, attorney for Vachel Dillingham, ordered that he have a permit to sell liquore and keep Publick House until next Court.
28	42-A	19 Mar 1799	On motion of Benjamin Clark ordered that he be permitted to sell liquors and keep publick house until May Court.
29	45-A	16 Jul 1799	John Clark, clerk of Christian County Court, having entered into bond in the penal sum of [left blank] with Benjamin Clark his security conditioned as the law directs and ordered to be recorded.
34	3	15 Oct 1799	Benjamin Clark with his security entered into bond with his security John Clark to Keep Tavern for the space of one year from this date conditioned as the law directs.
	5		On motion of James Wilson, Sheriff of Christian County, Thomas F. Elliott was admitted as his deputy sheriff he having taken the oath prescribed by the Law and constitution and entered into bond with Benjamin Clark and John Clark his security in the penal sum of 1000 pounds current money of Kentucky for the due and faithful performance of his office as deputy sheriff for said Wilson.

John CLARK is Benjamin's brother; Vachel DILLINGHAM is his father-in-law.

10b.  Lon Arneld Bostick, Sr.  1987.  County Court Order Book "B" Part 1 for Christian County, Kentucky, for the years 14 Oct 1805 - 12 Sep 1809 for a County Court held at Town of Hopkinsville. Christian County Family and History Research Society (4465 Cadiz Rd., Hopkinsville, KY 42240).  First column is the page number in Bostick; second column is the page number in Court Order Book B.

p.	p.	Date	Motions
52	109	12 Oct 1806	On motion Isaac Clark, Benjamin Clark asignee of Christopher Rider was admitted to remove his certificate of 400 acres No. 448.
96	205	7 Dec 1807	On motion John Clark ordered that Isaac Clark and Vachel Clark of Livingston County and Henry Clark, Jr., of __?__ County being sons and heirs of Benjamin Clark, Deceased and John G. Campbell, Edward Bradshaw and Zeba Howard commissioners who in conjunction with the heirs of Benjamin Clark aforesaid do make the aforesaid John Clark a deed of conveyance to 200 acres of land lying in Christian County agreeable to a bond given from said Benjamin Clark dec'd in his lifetime to said John Clark in the manner prescribed by Law which bond aforesaid is ordered to be recorded.

11.  Mary Clark's web site:  Genealogy of the Clark Family. 

12.  Pension application of Capt. John Wheeler, mentions serving under (then) Lt. Benjamin Clark; describes campaigns. 

13.  William S. Bryan & Robert Rose.  1876.  Pioneer Families of Missouri. Bryan, Brand, & Co., St. Louis, MO (reprinted 1997, Gen. Publ. Co., Inc., Baltimore, MD).   Biograpical sketch of Benjamin's brothers, Isaac and John, which mentions on p. 246: 

Benjamin died in Kentucky, and his widow moved to Boone county, Missouri.

There were no CLARKs, at all, in the 1830 Census of Boone Co., MO.  It appears that Patience went to Cole Co., MO, with her children and is living there with her son, Ephraim, in 1830.. 

14.  Thomas Jefferson Gregory.  1913.   History of Yolo County, California.  Historic Record Co., Los Angeles, pp. 695-696.  Brief mention of Capt. Benjamin in a biographical sketch of his grandson, the Hon. Ephraim Clark. 

15.  Descendants of Robert Dillingham, Sr. [link died] by Larry Wayne Lieneke.