(Looking back, I have to wonder at my child-self's absolute persistence in not taking my mother's "no" for an answer, even though to her knowledge she was telling the truth. She must have thought I was a strange little kid cross-examining her like that!)
Anyway, that persistent feeling of a "missing sibling" remained until I stumbled upon a television show that discussed vanishing twins. The knowledge was like a bright light being turned on and I finally had my answer!
Here is the introduction to that same show: