How can a nonparticipating mineral owner find out the name of the surface owner, lease holder, and other mineral owners of a specific section and block?
Contact a local title company in Reeves County.
That research is what they do.
All the information in the courthouse records is public information, but as an ex-surveyor, I can tell you it can be a major, time-consuming job tracking down chains of title and leases, etc.
Title companies are specialists at this plus they do have their own resources which make them more efficient.
Good luck!
You can also search the Reeves County, Texas CAD site, but it really just tells who the tax statements go to, and a title search is the only way to know for sure.