Do you have a birthday or state of nativity?
There is a William J Smart that was born 1822 in Pennsylvania that is listed on the 1860 census in Sullivan MO. Presumably he is the gentleman that enlisted in the Sullivan Home Guards in 1861.
The following are the NPS unit descriptors which help separate likely participants.
1st Battery, Arkansas Light Artillery (Union)
Organized at Fayetteville, Ark., and Springfield, Mo., January to August, 1863. At Fayetteville, Ark., January to April, 1863. Moved to Springfield, Mo., April 25-May 4, and duty there till September 21. Expedition from Springfield into Arkansas and Indian Territory September 7-19. Near Enterprise, Mo., September 15. Moved to Fayetteville, Ark., September 21, and duty there till March, 1864. Attached to District of Southwest Missouri, Dept. Missouri, to March, 1864. 2nd Brigade, District of the Frontier, 7th Army Corps, Dept. of Arkansas, to January, 1865. Artillery, 3rd Division, 7th Army Corps, to February. 1865. 1st Brigade, 3rd Division, 7th Army Corps, to August, 1865.
SERVICE.-Actions at Cross Timbers, Mo., October 15 and 20, 1863. Moved to Fort Smith, Ark., March 19, 1864. Steele's Expedition to Camden March 23-May 3. Prairie D'Ann April 9-13. Van Buren April 12. Camden April 15. Poison Springs April 18. Jenkins' Ferry, Saline River, April 30. March to Fort Smith May 3-16. Garrison duty there and at Fort Gibson till August, 1865. Action at Prior Creek September 18, 1864. Mustered out August 10, 1864.
35th Regiment, Arkansas Infantry (Confederate)
35th Infantry Regiment [also called 22nd Regiment] was organized during the summer of 1862 with men from Yell, Sebastian, and Perry counties. It was formerly the 1st (Rector's War Regiment) Arkansas Infantry. The unit was placed in Fagan's and A. T. Hawthorne's Brigade, Trans-Mississippi Department, and was active at Bayou Fourche and Helena where it reported 75 casualties. Later it saw action at Jenkins' Ferry and in April, 1865, disbanded. Its commanding officers were Colonels James P. King and Henry J. McCord, Lieutenant Colonel John W. Wallace, and Majors John J. Dillard and Mark T. Tatum.
Both these units have a William J Smart on their roles.
Looking back at 1860 Census records
1. William Smart, Marion, Sebastian, AR 17 abt 1843 Arkansas Male
2. William Smart, Jefferson, Carroll, AR 40 abt 1820 North Carolina Male
Thus I think the link is most likely #1 belongs to the 35th Arkansas Infantry.
The only William Smart with a record that I could find that clearly placed him at Pea Ridge/Elkhorn Tavern was on William Smart in the 24th Missouri Infantry. His card is here: http://www.sos.mo.gov/TIF2PDFConsumer/DispPDF.aspx?fTiff=/archives/AdjutantGeneral/Civil_War/ServiceCards/s859/0142.tif&Fln=S290088.pdf
Of note it marks him as died June 10 1862 Batesville Arkansas. Enlisting at Rolla Aug 20, 1861 but not mustering until Oct 14 at Benton Barracks.
The William J Smart of the Sullivan Home Guards enlisted in June 1861 and the unit was officially disbanded Sept 20 1861. He is found alive and well remaining in Sullivan County 1880 census so he IS NOT the William Smart of the 24th Missouri.
Don't know if you follow all this but hopefully it helps.
John R.