It looks like that entire area, which is the size of Albania, only has about fifty people living in it. They're so far from everything else and there's few enough of them that they can just agree to do their own thing

There used to be a telephone exchange there between Adelaide and Perth 100+ years ago. I think the theory is that the time zone was there to prevent confusion at the exchange, especially since they would otherwise have sunrise at like 4:20am. Since there are only three or four communities there they have kept the local time zone and use it for local business. It has an official code (ACWST), but it is not officially recognised by the West Australian government nor the Australian government when it comes to timing things for government purposes.

It’s also used by a single town on the South Australian side of the border.

IST Indian standard time is like 30 mins offset FFS

Contrarianism I reckon

Honestly, I don't get why anyone would want their timezone not to be a round hour. Surely the extra complexity and increased chances of mistakes isn't worth it? Timezones are bad enough when they're a round number. And as the map shows, many places don't match their geological position, anyway, so it's not like being 15-30 minutes off is a big deal.