I found the legal briefs. But as it’s not marked for distribution I won’t quote them. I will mention some of the public documents the authors cited. (That should be okay, I hope!)
United Nations Convention on the Law of the Sea art. 29, Dec 1982 defines a ‘warship’ as:
a ship belonging to the armed forces of a State… under the command of an officer duly commissioned… and manned by a crew under regular armed forces discipline
For the United States ‘regular armed forces discipline’ means being subject to UCMJ.
Geneva Convention Relative to the Treatment of Prisoners of War art. 4, Aug 1949, and Geneva Convention for the Amelioration of the Condition of Wounded, Sick and Shipwrecked Members of the Armed Forces at Sea art. 13, Aug 1949, recognise that a State engaged in armed conflict may lawfully authorize civilians to accompany the State’s armed forces during armed conflict.
As long as the civilians don’t participate in belligerent acts of hostility they are protected. If captured they are prisoners of war and treated as such. If they partipate in hostile acts they receive no legal protections.
During WWII US merchants were armed with self defense arms. The ‘majority’ of WWII merchants armed were manned with Navy Armed Gun crews. Merchants did not partipate in belligerent acts. Armed merchants excercised the right of self-defense.
WWII Merchants that conducted belligerent acts were converted to a ‘warship’ under The Hague Convention No. VII of 1907. In more modern times other countries followed this pattern, i.e. UK during the Falklands War.
The conclusions were that a ship of State conducting belligerent acts must be registered and marked as such, under military discipline and under the command of a commissioned officer. Civilians may accompany the ship as long as they do not participate in belligerent acts.
That’s pretty much it.