This sounds a familiar scenario. I should note that if a template is only used to render a note content in a manner that is included in some other note (e.g. parent including only the link counts of each child note as set va the chid’s template) them make sure you’re exporting the containing note, within which use of the desired template will then show (or not).
BTW, selected note export will default to the note’s ‘normal’ location within the whole doc export but only if the doc has been fully exported once (this is how I do quick corrections for typos etc in aTbRef single pages). Otherwise you can export the file anywhere. I note this fact as if your note uses CSS, JS etc and is linked via a relative reference those links may not find their targets if not at the correct relative location.
Still, selected note export is a real boon.
Also, don’t overlook the Preview tab of the text pane.