I have a little information on your Rebecca Garrison. She may have been born in East Baton Rouge Parish. Rebecca, her mother and seven siblings were living in East Baton Rouge Parish in 1850. Apparently the father was deceased. The mother, Margaret, was born in Mississippi and the oldest child, John, was born in Mississippi ca 1829. The other siblings were: William [LA ca 1830], Mary [LA ca 1832], Jane [LA ca 1835], Alexander [LA ca 1839], Stephen [LA ca 1843] and James [LA ca 1848]. I found a death record for Stephen. His parents were listed as Margaret Erwin and Lawrence Lot Garrison. I also found a death record for John Henry Impson [the son, bn ca 1866 - died 8/3/1942 Livingston]. His parents were shown as John Henry Impson and Rebecca Ladiner Garrison. The Garrisons must have moved from East Baton Rouge Parish to Livingston Parish. John and Rebecca were in Livingston Parish in 1860 and 1870. The mother, Margaret Garrison, was also in Livingston Parish in 1860 [Springfield Post Office].
I will see if I can find anything further on these families.