Wow, you are correct. Rich Walling missed the June muster roll for Captain Thomas Arnold's detachment. I took a quick look at it (we have a print from the National Archives microfilm), and was able to find most of the names from Louis Wilson's list. At least half of the privates and one musician were African Americans. It is very clear that most of them were at Monmouth (although two were left sick at Valley Forge and perhaps one of those on command was with the baggage at Rocky Hill). Rhodes is noted "sick at Englishtown," and Moses Wickes "sick Princetown." (Was Moses Wickes left at Princetown on the march to Monmouth--or sent back to the Princeton hospital after the battle?) Sick could mean "sick" or lightly wounded. Capt. Arnold is listed as "Wounded Absent."
We also have a print of the July muster for essentially the same detachment. This time, however, it is listed as Capt. Jona. Wallen's Company. Capt. Thomas Arnold is listed after Wallen as "sick # Englishtown."
In Major-General Nathanael Greene's letter to his brother, Jacob Greene, 2 July 1778, he notes "I had like to have forgot to mention that the Rhode Island Troops were in Action and behavd very well. Capt Arnold is wounded in the Leg."
What is uncertain is whether Capt. Arnold's detachment fought with Varnum's brigade at the hedged fence (most likely) or were part of a battalion of picked men (temporary light infantry). Maj. Simeon Thayer, 2nd RI, was wounded while serving as major of a battalion of picked men led by Col. Joseph Cilley, 1st NH. Cilley had men from 20 different regiments with him. Washington had sent Cilley's and Parker's battalions of picked men to attack the British right as it withdrew from the field at the end of the day.
I would love to have more particulars on these men. Do any of the primary sources reveal more about the Battle of Monmouth? What about the other men in the detachment? Which are WASPs, which are Native Americans?