OK, in the end, I had to create a new template for the home page rather than using the list.html for everything.
Slightly annoying since only 1 line needed to be different. I expect there is a more elegant way to put it all in the list.html template but time is short.
You seem to need this for the home page (home.html):
{{- $paginator := .Paginate (where .Site.RegularPages.ByLastmod.Reverse "Section" "!=" "") -}}
And this for all other section home pages (list.html):
{{- $paginator := .Paginate (where .Data.Pages.ByLastmod.Reverse "Section" "!=" "") -}}