Have you tried looking in the New York Continentals? There were three companies of New York’s 3rd Continentals operating in the area and time you describe. They were under the command of Lt-Colonel Henry Brockholst Livingston of Clermont, Duchess County New York. Often they are referred to as Whale boat men during this time. They helped evacuate persons, possessions and livestock off L.I. to CT. They caused great disruption for the local Tories and British regulars.
There is a John Bailey who appears on the 1775 Brookhaven Tax list paying 10 shillings 2 pence on his property. The area is on the north shore of long Island NY and the area’s small cluster of towns collectively were often referred to as being Brookhaven. Today the area is known as the 3 village Area on the North Shore of L.I. This is just a little to the east of Huntington.
There is also a John Bayles who appears in the 1776 census along with a wife, 9 children and also with two slaves. Perhaps a miss or alternate spelling? You should at least consider it.
John Bailey’s name appears in Colonel Josiah Smith's First Regiment of Minutemen of Suffolk County. After the Battle of Brooklyn Heights, the remaining contingent of Col. Josiah Smith's shattered NY Regiment numbered only 35 men. They were encamped at New Haven, Connecticut with Lt-Colonel Livingston’s NY Continentals, some volunteers and Colonel William Richmond's Regiment of Continentals from Rhode Island during October 1776 through November 1776. After that time I can not say.
You may also wish to try looking through information about the Setauket Spy Ring. As you probably know, the British Army had control of Long Island following the disastrous Battle of Brooklyn Heights. The out lying portions of the Island were patrolled by Tory bands and the majority of the population was Tory in sympathy. An excellent spy ring was however, able to be set up on the Island by the few Patriots remaining. One of theses I believe was John Bailey.
Washington had appointed Benjamin Talmadge head of his secret service and he established an espionage network against the British in New York City and Long Island areas. The undercover operation on Long Island was extremely successful. He and his operatives choose friends and neighbors from Setauket (Brookhaven), both men and woman. The Setauket Spy Ring was maintained so well some operatives were not uncovered until the 20th century. Col Livingston would call upon this service in planning his raids there. You may wish to look through the Colonel’s correspondence.
Of course, if a member of the ring, much of what he would have done would have been secret and only those participating in events were the only sources to corroborate his actions. This would explain the great difficulties many had proving their service for a pension after the war. Many would seek their former officers, unfortunately most had passed away. In this case, Talmadge or Washington may have mentioned his name somewhere in their writings. A long shot but you never know.
I hope this little bit has been helpful. If I can still help don’t hesitate to call upon me. Good luck!