I looked for her in the birth records, and found an infant Ramshay born on her birthdate, in Collin County, to a mother named Will. This was only an index of birth records, so that was all it had; to see more information, I'll have to see the actual birth certificate, which is not on the internet. I called the Texas Vital Statistics office, and they said I can send in a request with the certificate number (which was in the index I saw), or visit in person in Austin. Day trip to Austin, anyone?
My friend started helping me, and we found a cemetery listing in Bethel Cemetery in Collin County for Katie B. Ramshay and Infant of Katie and Joe Ramshay. I think we're getting warmer! Then we found death certificates for both Katie and the infant; they died in 1920, which may explain why I can't find the Ramshay family in that census. Also learned from that certificate that Katie's maiden name was Cole. I called my great-aunt Hazel and asked her if Ethel was about 6 1/2 when her mom died, and she said yes; also, that her mother was still alive when Ethel saw her carried out on the mattress to the hospital. This is exactly what the death certificate says, that Katie Cole Ramshay was in the hospital for 3 days before she died. Poor woman, in labor for 3 days (at least, who knows how long she labored at home before being carried to the hospital, most kids were still born at home in those days) and ending in both her death and the baby's. I can't imagine what her family must have gone through.
Looking in the Collin County records that are online, I've found an "Amendment to Certificate of Live Birth" for Ethel Marie Ramshay. It doesn't list her parents, but it confirms her date and place of birth (11 Nov 1913, Frisco, Collin Co., Texas), and it lists as supporting documentation an affidavit by C.B. Cole, her uncle.
Then I found a "Delayed Certificate of Birth" for Flossie Ramshay, who was Ethel's sister. This lists her parents as William (Will) Ramshay and Katie Cole.
Then I found a listing of a marriage record for Katie Cole and Joe Ramshay in Collin County, recorded 1 Jan 1911. Were Will and Joe the same guy?
I also found a "Delayed Certificate of Birth" for John Ramshay Jr., born to John Ramshay and Francis Irene Hassell in Frisco, Collin County, on 17 March 1919. Yay, cousins!
SO. I think I've found Ethel Marie Ramshay's family, but I don't have that one last bit of proof I want: Ethel's birth certificate stating who her parents are. What I DO have is that her uncle's last name was Cole, Ethel's mother died in childbirth when she was 6 1/2, and Katie Cole Ramshay died in childbirth when Ethel was 6 1/2. Is this enough information to say for sure that I've found Ethel's parents?