I'm not sure if EGG ever answered these questions, or was asked. I've always assumed he based it on what the ancient Greeks and Romans wrote about the Celts, and then added in a Greek mystery cult flavor to round it out. From Wikipedia, for druid:
The modern English word druid derives from the Latin druidēs (plural), which was considered by ancient Roman writers to come from the native Celtic Gaulish word for these figures. Other Roman texts also employ the form druidae, while the same term was used by Greek ethnographers as δρυΐδης (druidēs). Although no extant Romano-Celtic inscription is known to contain the form, the word is cognate with the later insular Celtic words, Old Irish druí ‘druid, sorcerer’, Old Cornish druw, Middle Welsh dryw ‘seer; wren’. Based on all available forms, the hypothetical proto-Celtic word may then be reconstructed as *dru-wid-s (pl. *druwides) meaning "oak-knower". The two elements go back to the Proto-Indo-European roots *deru- and *weid- "to see". The sense of "oak-knower" or "oak-seer" is supported by Pliny the Elder, who in his Natural History considered the word to contain the Greek noun drýs (δρύς), "oak-tree" and the Greek suffix -idēs (-ιδης). Both Old Irish druí and Middle Welsh dryw could also refer to the wren, possibly connected with an association of that bird with augury in Irish and Welsh tradition (see also Wren Day).
And for ovate:
Ovate in English is a borrowing and adaptation of a Greek rendering of the same Celtic term *wātis, first attested in the work of the Ancient Greek writer Strabo. Strabo rendered the Celtic term in Greek as ouáteis (οὐάτεις) (pronounced [ˈwaːteːs]). The English word ovate is pronounced the way it is due to a misunderstanding of how the Greek word was pronounced.
Ancient Rome The earliest Latin writers used vates to denote prophets and soothsayers in general; the word fell into disuse in Latin until it was revived by Virgil. Thus Ovid could describe himself as the vates of Eros (Amores 3.9).
In pagan Rome the vates resided on the Vatican Hill, the Hill of the Vates. The Vatican Hill takes its name from the Latin word Vaticanus, a vaticiniis ferendis, in allusion to the oracles, or Vaticinia, which were anciently delivered on the Vatican Hill. (When the papacy was returned to Rome from Avignon (France) in the 14th Century, the Vatican became the residence of the Pope, and the word Vatican came to refer to the enclave in the middle of Rome that had become the seat of the Roman Catholic Church.)
Celtic civilisation According to the Ancient Greek writers Strabo, Diodorus Siculus, and Poseidonius, the vates (οὐάτεις) were one of three classes of Celtic priesthood, the other two being the druids and the bards. The Vates had the role of seers and performed sacrifices (in particular administering human sacrifice) under the authority of a druid according to Roman and Christian interpretation.
And for hierophant:
A hierophant (Ancient Greek: ἱεροφάντης) is a person who brings religious congregants into the presence of that which is deemed holy. The word comes from ancient Greece, where it was constructed from the combination of ta hiera, "the holy", and phainein, "to show". In Attica it was the title of the chief priest at the Eleusinian Mysteries. A hierophant is an interpreter of sacred mysteries and arcane principles.
The idea of initates and circles seems to come from Wiccan witchcraft, but I'm completely ignorant about all of that stuff so I could be wrong. For all I know it could be inspired by the Masons.
This guy should certainly make an appearance in someone's campaign, as an Arch Druid
I think it has to do with lodge mentality mixed with the level mania of everything D&D which is just another part of the Gygax mentality of design as multi-layered and more for possibilities if things are mysterious and hidden.