Simple ternary da capo structure

[David Sumbler]

It's a while since I did much on Lilypond, but I have now started a new small project.  I am running xubuntu 24.04, and to keep things simple I have installed Lilypond from the distro's repository - version 24.3, which is pretty up to date.  There seem to be quite a lot of new features in Lilypond since I last delved into it, including \section and \fine.

I am trying to set a simple piece in ternary form.  I want a light double bar (thin-thin) at the end of the 'A' section with a "Fine" marking, and at the end of the 'B' section I want a full (thin-thick) double bar with "D.C." marked (or perhaps "D.C. al Fine", which is what the original has).

Section 1.4.1 of the Notation Reference has numerous complex varieties of repeats and dal segnos, but I haven't yet managed to get the result I want.  I'm sure it must be quite simple, but could someone show me how it is done, please?

David