It's a windows app, however, I figured it out just a few minutes ago. The confusion stemmed from the nomenclature used by Mercury.
There's a .click method, but no .dblClick method.
Apparently "Activate" is what's used for "double-click". It also either doesn't record, or only records as a .select with my current settings.
Since "Activate" seems to work, I can just use the code I've already written to return all the text in the tree, parse it, and double-click (i.e. activate) whatever I need to that way, or just use a hard coded string.