A lot of Richard Whites in that search....do you have any other details that would narrow the options...occupation? Address? Age? An example of said eccentricities ?
Richard White approx. 65 & Henry Clayton approx. 42, had travelled to the UK with various family members on board the brig 'Adelaide' They were business partners from what I can determine and were exporting bales of wool. More importantly they had travelled to the UK for the wedding of (the ship's master) George Dryden and Richard's grand daughter Sarah Jane White (daughter of John White).
Richard was a half American Negro who classed himself as a 'gentleman'. He was a wealthy land owner and had built the Launceston Hotel in Tasmania in 1822 (the first hotel) He was a keen gambler and a sharp dresser and would often be seen in Wellington Boots, white buckskin breeches, frock coat, top hat, wearing eyeglasses and carrying a walking stick. Eccentric in his ways and perhaps a little comical as well as an enthusiastic fiddle player. Also, his eccentricities "consisted in an assumed liberty of conversation to great and small"
Hope this helps. Thanks in advance