How to see current column/character number of the cursor position in Sublime Text 3?
I had missed something obvious! It turns out it is enabled by default - but is hidden if the search bar is open and has matches or if anything else is causing other information to be displayed in the bottom left corner. So, just remove whatever is putting info in the bottom left corner.
For example, here I can't see the column number:
...because it's replaced with information about my find box matches. Empty that, or close the box, and it's back:
Sublime Text top menu -> View -> hide / show status bar