S.W.
Hi, C.,
I have seen two births recorded on one birth certificate but that was in NYC in the 1910's. I can't imagine that it was legal in California to NOT issue a birth certificate. All states collect vital record statistics [birth, death, marriage, etc.] Surely, you went to school where proof of birthdate is required.
I would try your elementary school [or school district] for your cumulative file. A photocopy of your birth [birth certificate, baptismal certificate, or passport] should be included or since it was 1961 there might not be a copy but there should be a notation about what was provided when you were registered. It is a starting point for further research.
What did you use to obtain your learner's permit at the DMV or your marriage license or a passport?
In Sacto, there are books with the indices of births and deaths reported to the state - you might try there as well. Perhaps the record before or after your brother will be you. BTW, what is your supposed birthdate? How close in age are you to your 'twin' brother?
Good luck. I will be interested to see what other moms suggest.