Michael,
I found a "Neal Brim" listed in Craven County. I'm not sure if this is your family. It list his mother as, looks like "Ansy White." This does not match the name that you mentioned.
Birthplace: NC
Race: Colored
Crave Co, NC, Ne Bern Township
ED 26
Page 16B
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Neal Brim 37
Lizzie Brim 23 Wife
Grace Brim 8 dau
Thomas Brim 6 dau
Alfred Brim 2 dau
White, Ansy - mother 50
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Regina