Final answer:
The element of the AEF structure that includes two types of forces, one to support combatant commanders and the other for home station operations, is called the Enabler Forces. These forces were a significant part of the AEF's effectiveness during World War I under General Pershing.
Step-by-step explanation:
The component of the American Expeditionary Force (AEF) structure that consists of two types of forces—those that directly support a Combatant Commander's mission, and those that are the minimum number needed for home station operations—is known as the Enabler Forces. Enabler Forces are crucial for ensuring that combat missions are adequately resourced, and that non-deployed functions at home bases continue to run smoothly. During World War I, the AEF, commanded by General John J. Pershing, embodied this structure as they augmented the Allied forces in Europe with both direct and indirect support, eventually fighting as an independent unit.
On capturing the essence of AEF's value in battle, it is worth noting that in battle, there are not more than two methods of attack—the direct and the indirect; yet these two in combination give rise to an endless series of maneuvers, which the AEF explored under Pershing's leadership. Moreover, a close relationship between military operations and the elements of war embodied by American preparation and troop leadership shines through, emphasizing the importance of an effective military structure that the AEF represented.