There may be problems with the sacrum (above the coccyx) or other parts of the spine which gives pain that appears to be in the coccyx, though the source is elsewhere. These problems are not well understood. One woman who wrote to me had had a coccygectomy because of pain when sitting. The operation did not relieve the pain, and she has now been diagnosed as having pain caused by scoliosis (sideways bend in the spine) and consequent strains and tissue damage.
Partly by excluding other possible diagnoses, partly by investigating the various possible causes of back pain.