2324 has been a Family Tree Circles member since Jun 2022.
NSW birth index says mother was Alice, not Ethel (middle initial is E so probably Alice Ethel)
HEFFERNAN PATRICIA M
10732/1920 [6 Feb]
THOMAS
ALICE E
ORANGE
which means this marriage is probably the right one (it's the only Thomas with an Alice 1900-1920)
7581/1919 [11 Sep]
HEFFERNAN, THOMAS
MURPHY, ALICE E
SYDNEY
Lindsay
From the Lachlander and Condobolin and Western Districts Recorder Wed 19 Mar 1919 p.1
Constable Thomas Heffernan did a smart and plucky piece of work on Friday. A pair of horses attached to van were noticed in full bolt, having started down the hill in front of Mrs Cuningham's residence. The driver succeeded in turning them towards the railway, when "Tom" dashed across the street and ran in front of them, causing them to slow down sufficiently to enable the driver to pull them up. But he had a very narrow escape from being run over. It was a test of pluck not many would undertake.