It wasn't Gilliam, it's Gillam.Your Rebecca was born in 1815 - not 1825 - at least that's what I have in my records.Rebecca's brother Josephus also married a Gillam (William Gillam's sister, Sarah).
Take a look in the 1850 census - Rebecca Ann and William Gillam are living in Boone County, Indiana.He is 37 and she is 35.In 1850, they had children Hiram, Nelson, Matilda, Mary, Sarah, Zachariah and baby Hannah.(The name is mistakenly listed as "Gillum" in the census.)
This is Rebecca's family:
WILLIAM MCJIMSEY was born 1791 in Pennsylvania, and died in Jasper County, Indiana.He married RUTH MOONEY April 25, 1811 in Miami County, Ohio, daughter of JOSEPH MOONEY and REBECCA FREEMAN.She was born January 25, 1795 in Kentucky, and died April 05, 1853 in Jasper County, Indiana.
Notes for WILLIAM MCJIMSEY:
Listed in the "War of 1812 Muster Rolls" William McJimsey was in Capt. Westfall 's Mounted Co. (Oct-Nov 1812), Ohio Militia.
Children of WILLIAM MCJIMSEY and RUTH MOONEY are:
i. JOSEPHUS J. MCJIMSEY, b. April 09, 1813, Near Dayton, Ohio; d. February 07, 1895, Gillam Township, Jasper County, Indiana.
ii. REBECCA ANN MCJIMSEY, b. February 07, 1815, Ohio; d. June 21, 1854, Indiana; m. WILLIAM N. GILLAM, February 19, 1835, Carroll County, Indiana; b. April 08, 1813, Franklin County, Indiana; d. January 17, 1862, Indiana.
iii. ROBERT MCJIMSEY, b. 1821, Ohio; m. ELCENA RECORDS; b. November 16, 1822, Ross, Ohio; d. January 02, 1912, Van Wert, Decatur, Iowa.
iv. WILLIAM MCJIMSEY, b. 1830.
v. ASA MCJIMSEY, b. 1832, Ohio.
vi. JOHN MCJIMSEY, b. 1838, Gillam, Jasper County, Indiana.
vii. LUCINDA MCJIMSEY, b. January 22, 1824, Ohio; d. October 26, 1898, Michigan City, La Porte, Indiana; m. PETER TANNER, February 11, 1845, Rensselaer, Jasper County, Indiana; b. November 22, 1826, Piqua, Montgomery County, Ohio; d. February 24, 1886, Michigan City, La Porte, Indiana.