Not surprisingly, you will not find the cache at the posted coordinates, but it's a good place to start. The posted coordinates will take you to the front of the Bee County courthouse. The grounds around the courthouse contain several informational signs, one of which contains the answer you need to proceed to the final coordinates. Examine the signs and plug the answer to the following question into the Certitude link below to get the final coordinates.
What is the first name of the son who was instrumental in the naming of this county?
You can validate your puzzle solution with
certitude.