Tracking down a family owned fastback

Carfax.com should be able to tell you the last city and state the car was registered in, for a fee. Try it and see if it works.

When you enter the VIN number use 0's to fill in the empty digits.

Try doing a Google on "Mustang Registry". You'll find a few pages like THIS; as well as smaller registries devoted to different 'sub-groups' such as year, body style, color, engines, etc.

I think the DMV would be the place to start. If not Let Mustang Monthly know about it , I think they would put something in their Magazine about it. Let us know what happens.

How long did she own the car?

Hate to say it, but unless she kept it until the '80s(or has records of it existing until then) when these cars started becoming considered collectible, it's possible it may have found it's way to a scrap yard.
I mean, if 1 million of these cars were built before the '66 model year ended, there's no telling if it even survived or not.

That said, if this were my car, I would love to have these documents. Even though my car won't go back to stock. The oldest documents I have on my car go to back to 1989 when the C4 was rebuilt at an AAMCO. I just have no interest in restoring a 200ci Smog equiped Antique Bronze 1966 Mustang back to stock.