What is dedjatch?

Solution 1:

In Amharic, the primary language in Ethiopia (or Abyssinia at the time of Rimbaud's writing), Dejazmatch or ጽጅዝምች (sometimes Dejatch) means literally

Keeper of the Gate

or more in terms of functioning role, translated as

Governor General

or even

Prince

The spelling 'Dedjatch' is presumably a francophone spelling ('dj' is how the French spell the rare in French voiced palatal affricate which is 'j' in English).

Searching for 'dejatch' yields many sources saying "Prince (Dedatch) Alemayehu" or just "Prince Alemayehu", and the interpretation that 'Dejatch' is a title of nobility works in all the contexts it is mentioned in those texts.

The usual term for 'prince' in Amharic is ልዑል= liuli, the son of the emperor. But translation and cultural choices can be arbitrary and the English (and French and Italian) somehow settled on 'prince' in this situation.

The list of titles of nobility in Abyssinia gives the real correspondence.