Can you describe the differences in product management positions at Google? Which ones are technical and non-technical?
In my case, I was clear that I was unable to relocate, which left only a specific position available as a possibility which was nearby. The reason I thought that specific position had technical responsibilities was by the description of said responsibilities in the job description as posted. Also, I was told that I was contacted by Google in large part because of my technical background, but during the interview, that background was not discussed or explored.
Sorry I couldn't be of more help!
After the hiring committee has decided whether or not to hire you, your specific background will be matched with specific openings around Google. Naturally, some products require less technical expertise than others.