As a former student, then reenactor in Ancient History (Roman Republic), can I give an indication ?
In Roman society, the stick, BACULA, is the real and more ancient sign of authority : shepherds had the PEDUM, schoolmasters had the FERULA, lictors had VIRGAE, centuriones had the VITIS... and OPTIONES had the HASTILE. That is a long stick finished with a metallic ball.
The OPTIO was the centurio's assistant. In battle, he stood behind the ranks, to keep the formation cohesive and aligned. He also had the function of discouraging runaways. At camp, he served as sergeant-major (adjudant-chef de compagnie) : he was responsible for discipline and acted as administrative NCO. The centurio was the brave leader, the father of his troopers ; the optio was the oldest brother... Together, they had what Romans called POTESTAS and AUCTORITAS, the divine power of "life and death" and the human right to command and punish.
In Roman society, former optiones often formed the basic structure of police forces (VIGILIAE) in Roman cities. Others were employed as administrators and executive officers in prisons, mines and State yards, ports and ships, as tax collectors, and so on... In the army, some could become SIGNIFERI (standard-bearers), others CENTURIONES.
This stick, HASTILE, is not a weapon stricto sensu, but a honorific (mark of rank) and utilitary (you can hit your men) sign of power.
Regards.