Will it be available immediately when editing ANY template, just by giving the name of a page using the template, and without having to go to a special page ?
The idea would be that we could have just before the edit comment field a field that contains the name of a page to see, and that the "Preview" button will preview that page instead of just the template page itself.
Then an edit link somewhere on a page could prefill that field with a test page name (with an edit parameter). Notably, in the Template space, it could be prefilled with the name of a "/test" subpage where it exists, otherwise it will continue to preview the main template page transcluding the /doc subpage containing the examples of usages (but generally these examples do not contain an extensive list of rendering tests for complex tests.
E.g. of a normal edit link adding the test page in parameter:
And to format the edit link using Wiki syntax :
[{{FULLURL:Template:Example|action=edit|testpage=Template:Example/test edit]
In other words, no need to visit a special page, but a full integration in the standard page edit form (independantly of whever the edited page is in the Template namespace or not), using the specified (or manually entered) test page directly with the Preview button.
When editing an article in the main namespace, or a talk page, with the top "Edit" tab, no testpage would be prefilled but the testpage field would be there at the bottom of the edit form, where one could still manually enter the name of a test page (its default value would be the edited page itself, to make easy to append the name of a subpage).
When this form field is erased or contains the name of an inexistant page, its value would be replaced by the name of the currently edited page and the Preview page would refill that field and the preview page would also indicate the name of the test page it uses for rendering the preview (it should also say to the user with a warning that the name of the test page does not exist, before displaying the rest of the rendered testpage).
As well, when using the edit links above, if they don't specify the name of the testpage, or if they specify an inexistant page, the same warning would be displayed before the edit form, and the form would still be prefilled automatically with the name of the edited page as the default name of the test page.
So there's no need for a special page. The name of a test page would be present in all edit forms from any page in any namespace.