Secretive or not, the woman must be in some census records. Those have clues as to age, birthplace, spouse, children, and more. If you can’t find hers, look for birth and death records for her children which often list mother’s maiden name. Is there a marriage record? Sometimes you have to collect all the records that are possibilities, then make a timeline and/or a map to see what fits. Brown is a really common name so you may end up at a brick wall, but you will probably know at least a little bit more than you do right now.