In the pre - internet days of 1993 I had the same problem except I had an owner card with the name and address of the original owner. Which you also have.
I went to the local library and asked how I might find that person. The librarian gave me a whole list of options to try including the Social Security death rolls, City of Dallas directories, reverse lookup phone books, and several others including Dallas Morning News subject listings and Delta Airlines retirement rosters.
I found a whole litany of results on that person and her previous addresses and employers which eventually, after many phone calls, led to me finding her and meeting her.
If your mother can remember who she sold the car to you can probably find out where it went. I highly recommend using a librarian they know plenty!