You might try a post on both asking for an obituary look-up. If you do, PLEASE mention on both that you have cross-posted, and post a copy of the first response you get on the other one. Otherwise, some kind-hearted soul who does lookups on one will duplicate the efforts of another KHS who does lookups on the other. I do lookups for my county, and I know what I'm talking about.
The obituary should mention survivors and what city they lived in in 1992.
has 52 people named Mobley in and around Cairo, the County seat. (I used it and the "nearby area" option because I didn't know what town in Grady County to use.) That is too many to call, unless you have a lot of spare time and a really great long-distance plan. Once you get a first name and a city, though, you could try. You might get an uncle.