And a little mystery has been solved!!
What I wrote
 in early June 2004

I have to believe that Woody was a pal of Master Trebilco, and that he was returning to Australia from ... where? ... England?
Perhaps he and his family were emigrating, and young Trevor had reached Melbourne first.  We'll probably never know as the stamp dates this postcard prior to 1937. 

What I received on
 30 July 2004
Michael Fitzgerald

Hullo Richard,
Peter Trebilco phoned me today to confirm that he is the "Master Trebilco" of the postcard published on your site. He is an old friend of a cousin of Sylvia, my wife, and now lives in Sydney. He has been in Europe for some months, hence the delay in telling you this.
Peter tells me that Woody who sent the postcard was his great-aunt, Ethel Mary Woodcock, who was known as "Woody" to all. She was born around 1875 which would put her in her fifties when the card was sent. Apparently she was unmarried, a great traveller and something of a character.

Stretching coincidence even further: When I first rang our cousin, Jonothan, who lives in the Blue Mountains about the postcard he answered from Peter Trebilco’s home where he was house-sitting while Peter was abroad! He had had his phone calls diverted there.
Thanks again for your ‘Tiki site, it has given me much pleasure, not least hearing from an old shipmate, David Webber.
Please note that I have resisted the temptation to talk about a "small world."

A Final comment:  This is an amazing tale not least because the postcard itself is approaching 67 years of age.  In addition, the card was mailed in Jamaica to a correspondent in Australia, yet was purchased by me from a US seller.  Now ~ if only the card could tell the tale of its travels!