re: Tasmania, a search here on Honeyball comes up with a will for his father, James Frederick Honeyball, in 1925:
https://linctas.ent.sirsidynix.net.au/client/en_AU/names/While he is listed as of Teynham, Kent, but for his will to be probated in Australia suggests he had property there.
J F M Hearne's notice in Australia says letters of administration
resealed in NSW, which suggests he didn't die there; resealing happens when probate/administration proceeds in one country but there is property in another. I do not think he died in Australia, mostly likely in Guernsey. Unfortunately I don't think
https://probatesearch.service.gov.uk shows also a reference in 1969 for him, late of Glen View, Fermain Road, St Peter Port (over twenty thousand pounds in the UK alone!)
He enjoyed his cars:
http://trove.nla.gov.au/newspaper/article/67120964?searchTerm=Hearne%20Honeyball&searchLimits= - 1924, in Tasmania, as "Mertyn Hearne Honeyball"
http://trove.nla.gov.au/newspaper/article/29117386?searchTerm="Martin%20Hearne"
- 1925, Tasmania
http://trove.nla.gov.au/newspaper/article/154055006?searchTerm=Hearne%20Honeyball&searchLimits=
http://trove.nla.gov.au/newspaper/article/91624352?searchTerm="Martin%20Hearne"
http://trove.nla.gov.au/newspaper/article/51367981?searchTerm="Martin%20Hearne"
- 1926, the last shows him with the "Hearne" rather than "Hearne Honeyball" name
www.britishnewspaperarchive.co.uk has a few interesting hits for "Martyn Hearne" including some later ones for J. F. Martyn-Hearne in Sussex papers which make me think he didn't spend all that much time actually residing in Australia. I believe he is in the UK for the 1939 register, as "Martyn J F Hearne", living in Brighton.
Most interestingly, in 1925 there is an engagement notice for Martyn Hearne Honeyball, this is from the free search:
The engagement is announced of Martyn Hearne Honeyball, elder son of the late Colonel J. F. Honeyball, V.D., J.P., and Mrs. Honeyball, Newgardens, Tcynhani, Kent, to Rachel, only child of Dr. and Mrs. A. Irby Webster
Alfred Irby Webster married Agnes Eliza Jackson and their only daughter was Rachel Irby Webster:
https://www.familysearch.org/ark:/61903/1:1:XW6S-KK2Sadly Rachel Irby Webster died, unmarried, in 1929, so it appears the marriage never took place.