The Pope of the Catholic Church is an absolute monarch - Head of State of the Vatican City State. He is granted this title through an election by the College of Cardinals. See: The Pope...is currently the only absolute monarch in Europe..
What other historical examples do we have of such a system of government being successfully implemented: An absolute monarchy where the monarch does not inherit their title, but acquires it by virtue of election, when the previous monarch dies, or abdicates; or perhaps even a system where a true monarch is elected for a term of office?
Clarification: I agree with the comments: The term 'monarch' here is unclear.
Monarch is from the Greek: < Greek monárchēs sole ruler; see mon-, -arch -
So an absolute dictator could also be called a monarch in that sense. On the other hand, modern usage seems to reserve the term for someone who inherits their position - "Royalty", although they may have little temporal power.
In this context I will distinguish between a "monarch" and a "dictator" or "despot": Monarchy is an agreed upon institution of a sovereign state, established by long standing tradition or constitutional process, as per Edmund Burke's principles. This reflects Mark C. Wallace's comments "a monarch has legitimacy and accountability" - not simply an individual who seizes power for the moment.
As for "absolute", let's go with the vernacular of "Their word is Law". Or to take it to extremes, as has been attributed to Louis XIV: "The State? I am the State!".