Hi Jeanette , had a look at NSW Archives , and also can't find him arriving (tried some of the Manx variants - Hamson,Hanton & Honton), too late to be a convict !!! I have two families , one in the 1850's and one in the 1880's , both who ended up in Newcastle NSW , that I also cannot find arriving . I went through all arrivals at the State Archives Office in case they had come from the U.S. , but still could not find them.
However did find a lot of people arriving from North America , who had been born in the UK , had children in Nth America , and came to Australia , so it is worth a look. The ships coming from North America are not online or indexed- you have to go ship by ship !!!
Also on this site is a posting from Lynda Hampton Peters , from 1/5/2007, her Grt Grandfather was Samuel Hampton , younger brother of your Thomas J , She states Samuel went to the US in 1880.

Hope this helps
David Dwyer
Manly, Sydney