Pausanias on Achaean armament, ca. 200 BCE

[PMBardunias]

Light Infantry has many other roles, as I have explained already, among them they support skirmishers (that is why Polybius mentions so many times "Peltastes and Euzonoi" acting detached in advance of the main force), and they are picked men, either as a consolidated unit (when they receive specific training ) or as selected members of line infantry.

This is why I think the term artificial. What you are describing is simply line infantry trained to support skirmishers. They can either fight as skirmishers, by throwing things or engaging in a disorganized squabble, or clash while spontaneously forming a battleline.

Open order is a formation that allowed fast, fluid movement of the formation, yet keep enough order so that it could be redeployed in a closer one to face enemy in close combat, for example the Peltasts crossing a river as a vanguard and the closing ranks to repel a cavalry attack.

When in early modern armies, all infantry were skirmishers who fought with missile weapons, open and close is a valid distinction- they only become battleline infantry in the ancient sense when they charge with bayonettes. In the period we speak of there is no opened order battle. It refers simply, as you note above, to the formation you move in. No matter how you get there you must form a battleline to fight a battleline or skirmish against skirmishers.

Mobility is limited by two things, arms and training. Thus well trained hoplites could race to the tops of hills while musket armed French conscripts were packed in columns to advance. The "light" term cannot be consistantly applied because it is relative. To a late sarissaphoroi all thureophoroi and romans would fit your definition since they could be more mobile and throw things if need be.

Many troop types have the ability to do both in some capacity. What you are describing as "light" is simply line infantry trained to a dual-role function.