Hi, Blue,
Yes, there is evidence of Henry having been a bricklayer, on birth registrations here in Australia for 2nd and 3rd children Jean and Henry, and also in an 1889 Rate Book in Melbourne.
DNA evidence also points to Henry Brookfield b 1859 in Churchtown to John Brookfield and Catherine Rimmer as being correct.
There was similar speculation in our own family of him having been related to Percy Brookfield, the politician from Broken Hill who was murdered in South Australia. When I researched Henry 1859's immediate family, I had come to a similar conclusion, that Percy and Henry were not related.
Percy was however the great nephew of John Orlando Brookfield, who was a miner on the Bendigo goldfields.
Cheers