Neither of these lines is in my direct lineage within the last couple of centuries, but I do have a couple of leads for you.
According to my records, your grandparents were Samuel E and Edna V (WILBORN[E]) THIGPEN. Sam's ancestry can be traced through one of the early THIGPEN migrants to Texas, the variously and multiple named, William Walter James Norwood THIGPEN.
I have traced the lineage of M Anita (THIGPEN) PERRY back to Joseph B THIGPEN (b.1882) of Mississippi. Again, since this is not my direct line, I have not spent a great deal of time researching it.