I have quite a bit of information pertaining to the various THIGPEN families in Texas. There were many, so if you have any additional information that may provide further clues...
For Eastland County I only have a couple of facts that may be of help in your search. The 1920 Federal Census for Eastland County shows two THIGPEN entries. One is the family of William P. THIGPEN and the other is for an individual, Sophie THIGPEN, residing as a border in the household of Terry A. BRASWELL. Also, there were several THIGPEN families in adjoining or nearby counties.
Given the reported date of birth for your grandmother, I would guess that, if there is any relationship at all, these individuals may have been siblings or cousins. Further, there do not appear to have been any THIGPEN households in Eastland County in either 1900 or 1920 - at least not indexed in the Soundex for those years.
I would be interested in discussing your THIGPEN ancestors a bit further, if you are interested please contact me by private eMail: <Herman.May@earthling.net