Flinders
It may seem strange, but my wifes ancestor the Rev Jonathan Eastwood came down from Eccesfield in Yorkshire where he was the curate to Hastings in 1864 to recover from TB - unfortunately whilst he was here he died in June 1864 and is buried in Hastings Cemetery in Division A, Section K, Row I, Number 9. which is not to far distant from your relative.
His address at the time of death was listed as The Rectory, Church Road on his death certificate - and having visited the address, it is right next door to the St Mary Magdalen Church (now the Greek Orthodox Church)
So it looks as though your ancestor trod a similar path to that of my wifes Great Uncle
Chris in 1066