On a real talk page, the "New section" link is part of the page's content actions, always. No matter whether one is reading the page, viewing its history, viewing its Page information, editing it, etc.
When using the __NEWSECTIONLINK__ magic word on other discussion pages (e.g. Teahouse, Village Pump, etc.), the link is only shown when reading the page. In other modes, the link disappears from the navigation menu.
Things like DISPLAYTITLE have the same issue; since it's tied into the rendered page view, other actions don't have access to the state setting.
(In reply to comment #1)
Things like DISPLAYTITLE have the same issue; since it's tied into the rendered
page view, other actions don't have access to the state setting.
One way to fix it would be to register DISPLAYTITLE and NEWSECTIONLINK in the page_props table.
As workaround is an additional API query necessary:
http://en.wikipedia.org/w/api.php?action=query&titles=Wikipedia:Village_pump_(technical)&prop=pageprops → typeof .pageprops.newsectionlink !== "undefined"
Tagging Growth team as this might be of interest to them. I can see this affecting new users especially with links sometimes showing and sometimes not.
The information for this is available in the page's properties which can be queried even without needing to deal with a possible-absent ParserOuptut entry.