Is it possible that an australian 1967 Mk1 Cooper S could have had a non-self cancelling indicator stalk?

I don’t think so

More likely the column or indicator switch isn’t aligned correctly with the cancelling lug

_________________

The original Lucas switch is a 31945E made in 12/66. Does not appear to have the necessary 'projections' to be self-cancelling. Can anyone confirm this, please?

You’ll need to make sure:
The inner column is on straight. This is easy to spot, as when you are driving straight the pinch bolt at the bottom of the column should be horizontal. The cancelling lug at the top of the column should be at the “3 o clock” position

The two returning levers should be adjusted for height up and down, and for rotation so that the lug is in the centre. You can adjust this if needed by loosening the outer column bolt and rotating or moving up or down the outer column

This is a partially disassembled indicator switch. The part with the blue arrow is a sprung detent plate that holds the indicator in the turning position. The returning levers with the yellow arrow knock the indicator back to the centre and as mentioned above should be aligned in both axis with the lug on the column

_________________

Timmy 201. Thanks for photo. I think someone has had mine apart and re-assembled wrongly. Mine doesn't look like this.

What is the makers number on this, Timmy 201?

Same as yours - 31945E

If you need some parts I’ve got a few spares

_________________

Sorted thanks to your photo. Had to find a replacement for the tiny spring though.
Many thanks