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I've been investigating this time zone for a while, but this page (and the Eucla page) are the only places I've heard of it ever being officially sanctioned. I've spoken to people in Eucla on the subject, and the impression I get is uniformly that the local people decided to do it on their own. This is borne out by the comments in the time zone files:
# From Rives McDow (2002-04-09):
# The most interesting region I have found consists of three towns on the
# southern coast of Australia, population 10 at last report, along with
# 50,000 sheep, about 100 kilometers long and 40 kilometers into the
# continent. The primary town is Madura, with the other towns being
# Mundrabilla and Eucla. According to the sheriff of Madura, the
# residents got tired of having to change the time so often, as they are
# located in a strip overlapping the border of South Australia and Western
# Australia. South Australia observes daylight saving time; Western
# Australia does not. The two states are one and a half hours apart. The
# residents decided to forget about this nonsense of changing the clock so
# much and set the local time 20 hours and 45 minutes from the
# international date line, or right in the middle of the time of South
# Australia and Western Australia. As it only affects about 10 people and
# tourists staying at the Madura Motel, it has never really made as big an
# impact as Broken Hill. However, as tourist visiting there or anyone
# calling the local sheriff will attest, they do keep time in this way.