These entries are found in two sections of "Officers and Men of New Jersey in Wars 1791- 1815". It has long been believed that this Thomas was a son of William and Beulah Pettit of Burlington Co., NJ. There is nothing here to disprove the claim; however, more evidence is needed to prove the relationship.
from War with Great Britain, 1812-1815, p. 245:
Pettit, Thomas - Private, Captain Anthony Gale's Detachment; enlisted at Philadelphia, Pa., October 14, 1807, for three years; age 21; born, Burlington, N. J.; transferred to Headquarters, Marine Corps, Washington, D. C., December 2, 1807; private, Second Lieutenant Lee Massey's, Jr., Detachment, on Sloop-of-War "Hornet," Master Commandant John H. Dent, May 1, 1808; on rolls of Detachment to December 31, 1809; private, Second Lieutenant William S. Bush's Detachment, on Sloop-of-War "Hornet," Lieutenant Theodore Hunt, January 1, 1810; transferred to Headquarters, Marine Corp, Washington D. C., June 6, 1810; discharged, October 14, 1810, expiration of service; re-enlisted, at Baltimore, Md., October 23, 1810, for five years, as private, Sergeant Morris Palmer's Detachment; private, Lieutenant William H. E. O'Brian's Detachment, on Brig "Enterprise," Lieutenant Johnston Blakely, October 31, 1811, to April 30, 1812; private, Major Daniel Carmick's Detachment, at New Orleans, La., August 12, 1812; transferred to Sergeant Levi Derbin's Detachment, on Brig "Enterprise," Lieutenant Johnston Blakely, May 1, 1813; engaged in the capture of British Brig "Boxer," off Penguin Point, Maine, September 5, 1813; served to close of the war.
from War with Algiers, Africa, 1815, p. 16:
Pettit, Thomas - Private, Sergeant Levi Derbin's Detachment, on Brig "Enterprise;" transferred to Captain William Anderson's Detachment, at Navy Yard, Charlestown, Mass., May 22, 1815; transferred to Brig "Enterprise," July 5, 1815; transferred to Captain William Anderson's Detachment, at Navy Yard, Charlestown, Mass., July 22, 1815; on rolls of Detachment to September 30, 1815; discharged, at Navy Yard, Charlestown, Mass., October 23, 1815, expiration of service; re-enlisted, at Boston, Mass., October 28, 1815, for five years, a private, Captain Robert D. Wainwright's Detachment; promoted Corporal, January 27, 1817; died at sea, on Frigate "Congress," February 27, 1821.