Newspapers throughout Europe wrote about Mr. Adams' actions at Buitensluis, from the Laibacher Zeitung in what is now Slovenia, to the Scots Magazine. According to British sources, he was an Englishman, in German sources he was a traveling Englishman, curious to see a country liberating itself from the French, and Dutch sources wrote that he was a citizen from The Hague.
The Literary Panorama, Volume 13, printed a letter from him, dated November 30, 1813: "Most respected Sir, - I have ventured to march against a battery of eighteen pieces of cannon, with only fifty volunteers. It is the Buitensluis. I have taken it without firing a shot, and made sixteen gunners prisoners - Adieu, most respected Sir. "I am always entirely your's, (Signed) "J. Adams"
Interestingly, the letter is signed J. Adams instead of T.P. Adams. J. Adams would have been his father. Not sure what to make of it.

He would not have worn his old English uniform. When the envoy Charles Grant arrived in The Hague and started to wear his British Volunteer Corps uniform on 25 November, he was cheered by thousands of citizens as the first allied soldier. Adams had already been appointed on the 23rd, so he must have worn a civilian red coat.

The orange flag was just that, a completely orange flag. All orange clothing had been forbidden by the French, even wearing an orange cockade was considered an act of rebellion. An orange flag was quite something in 1813!

When Adams captured the Buitensluis on 29 November, there were no other Prussians in the area besides the 'Orange-Prussians', formerly of the 4th Regiment Etranger. These formed the first true soldiers of the new government. Most of them had started wearing orange cockades on 19 November after dismissing their French officers.

The first Prussians arrived in Rotterdam on 3 December 1813, probably von Colomb's Streifkorps. Von Bülow's troops arrived in the area later in December. Your volunteer must have been part of the latter.