What is the historical basis of diksa initiation?
In older literature such as the Bhagavatam, diksa refers to a process whereby a participant in a Vedic sacrifice, under the guidance of a qualified brahmana, performed special rites, austerities, etc. in order to reach a high state of consciousness prior to the sacrifice. As sastra explains, Vedic sacrifice brings us directly into the presence of God. So to prepare for that holy encounter, one had to be in the highest state of consciousness possible and the preparatory procedure was called diksa.
As bhakti became prominent as the real sanatana-dharma, one’s entire life was seen as the preparation for the supreme sacrifice of giving oneself fully to Krishna. Thus, diksa was not a short preparation for a specific sacrifice, but rather a lifetime vow for going back to Godhead. The Bhagavatam does famously say that in Kali-yuga the chief yajnas are sankirtana, and so by analogy sankirtana-diksa is implied.
In the Caitanya Caritarmta and other Gaudiya literature, we find more of the types of lifelong guru-disciple relationships that we are accustomed to. As far as I know, we do not find in the Bhagavatam, Mahabharata, etc. this diksa for life, giving a new name, etc. Although, these procedures are probably ancient.
Two-tier diksa seems to be a detail, applied to the general principle of bhakti-diksa.