While the Enneagram types are not ancient themselves, Ichazo apparently did borrow and find inspiration from a wide number of traditions he was familiar with. So although it can't be said that the Enneagram types are ancient, it can be said that elements of the types can be found in older traditions.
Oscar Ichazo hosted a months-long training retreat in Arica, Chile around 1970 where he introduced, among other things, what he called proto-analysis. Proto-analysis identified a person's ego fixation so that work could be done on finding some freedom from it. This was incorporated into a much larger teaching of methods for working on the self, part of his Arica School, which in 1971 found its way to the United States through the Arica Institute.
John C. Lilly and Joseph E. Hart wrote about some things they learned at that retreat which is included in the book Transpersonal Psychologies edited by Charles T. Tart. They mention nine ego-types and the fixations, traps, holy ideas, passions, and virtues associated with them. There was also mention of what later evolved into the instincts of the Enneagram personality types.
A psychiatrist named Claudio Naranjo attended the retreat as well. Naranjo took the ego-types down a different path than Ichazo and evolved them into the Enneagram personality types used today.
Each ego-type is represented by one of the nine numbers on the Enneagram symbol. The label for each ego-type combines the "Ego-" prefix with an abbreviation for the related fixation. Not only is each ego-type associated with a fixation but also a trap, holy idea, passion, and virtue as well.