Two more tips.
I have had some luck by searching with the keyword of the address, using no name. That has worked on fultonhistory.com. You might find a relative's name.
Also, I'm sure you know well that the first two boys and first two girls were usually named for the grandparents. Sometimes the father's parents first; sometimes the mother's; sometimes neither. I'd search NY for all possible spellings of Tompkins with the boys' names. Then search the census for those families. A lot of work but it may pay off in the census before she was married and might still be at home.