Can the Sphinx "automodule" be told to automatically insert section breaks between members?
No. There is no magic option to automodule
or something like that. If you want section headers then you'll have to add them yourself (perhaps by using a script) to the reST source. See also the answer to this similar question: Sphinx customizing autoclass output.
The Mayavi documentation that you refer to is not created with autodoc. The functions are documented using the function
directive (not autofunction
). Click on "Show Source" to see the reST markup.