At their VA hospital. How do I locate her adoption records?

You probably can't. Adoptions then were pretty much exclusively closed, and you'd need a court order to get it opened. That usually only happens in cases of extreme medical need.

You can register on reunion websites and you're welcome to hire a licensed private investigator.

Why is it you that is looking and not the parent?

I met my birth mom, because I registered, she registered, and someone connected the two posts and contacted us!
Oh hey... if the adoption took place IN Florida, there's a great chance that it was an OPEN ADOPTION. If not, mine wasn't, so I'll tell you that next step. Go on reunion registers, and put in as much as you can find, and pretend that she has just a little bit of information, too. "Search" for your mom that way. You might find where your sister had written, looking, as well.
If you have the money, go through Kinsolving. They are TERRIFIC at that sort of stuff. But be prepared: they can often have your answer within a week!

Actually, there's very LITTLE chance that it was an open adoption in the 1960s. It DID happen--but those people don't generally need to search because "open adoption" means that there is communication between the birth and adoptive families.

And without knowing WHY someone is searching for an adoptee of the 1960s, I can't support the search beyond a reunion registry--especially for a sibling! Too often, those adoptees do not KNOW they are adopted, and "finding" them without their knowledge or consent of the search means that you are creating HUGE issues for someone to deal with because they had no idea.

When both register--GREAT!

But when one party does not want to search or does not even know they are adopted--that creates real problems for people.

And we don't know why the SIBLING is posting, and not the PARENT. That usually means that the parent does not WANT to look, and the sibling is looking despite those wishes.