A very useful post Ken. At least part of the 16th Light Dragoons were in America (and 17th Light Dragoons) 1776 to 1778. At least parts of these two regiments were part of the infamous British Legion commanded by Lieut. Colonel Banastre Tarleton (local rank)(aka the butcher)(see 'The Patriot' on youtube). That was an all arms formation, infantry, cavalry and artillery mainly composed of American loyalists. Tarleton had been a junior officer in the Kings Dragoon Guards and went out to America with Lord Cornwallis. As the war went on, more and more regiments were withdrawn to UK as France, Spain and Holland came out against us.
Contrary to the fate of Tarleton in 'The Patriot', he was MP for Liverpool in the 1790's, promoted full general in 1813 and died in 1833. He was under consideration as commander in the Peninsular vs the future Duke of Wellington.
He is credited with the design of the 'Tarleton' helmet and worn by Light Dragoons from c1790 to 1811. Their red coats were replaced by blue shell jackets and this uniform was a particular favourite of King George III.