It would also be interesting to know about different ways commanders of all ranks behaved in combat.
e.g.
Fighting like everyone else plus shouting orders?
Fighting with a special guard; maybe as a driving battle factor?
Staying just behind the first ranks and observing/reacting?
Leading a special reserve to special situations?
At the very front of formations?
At the center of formations?
Just fighting? Just commanding? Just accompanying troops to places but then falling back before enemy contact?
It wasn't so much a matter of culture, but rather a matter of the character of the leader that determined if a high ranking leader would lead and fight in the battle. Alexander the Great was notorious for donning his flamboyant, shiny helmet and leading the charge into battle.
But that was rare for a high ranking leader. Normally, somebody of his statue would watch from a hill top, and give orders to couriers to deliver to the field commanders.