10 U.S.C. includes the Uniform Code of Military Justice (UCMJ) (near as I can tell), specifically I'm curious how the decisions made by the Secretary of Defense play into the (Section 891) Article 92 regulations.
Specifically, Article 92 acknowledges two types of orders that a soldier might end up in trouble for disobeying: general orders and other, specific orders.
On the face of it it would seem to me that an order from the Secretary of Defense carries the full weight of the Office of the President, and therefore the Commander in Chief as an order-giving entity that soldiers are obliged to obey.
This Wapo Article discusses the refusal of the OK Nat'l Guard to follow the order (on counter-orders from the Governor). I'll break out the separate, interesting question about DoD authority over Nat'l Guard units into another post.
But it makes me wonder: Would a general officer refusing to relay the vaccine mandate to the units under their command constitute disobeying an order under Article 92? If so, would an order like this from the Secretary of Defense constitute a general order or the more specific "other" case?