The facial elements of the signed 'Richardson's vitrified' 'Etruscan' style vase above are also different to the facial elements shown in Hajdamach with the Richardson mark and diamond registration. Maybe facial features aren’t a reliable indicator?
No they aren't. But there are other things - I can't explain exactly what, but there are
that can help to put the vase with Harrach or possibly Richardson's and also with Loetz or Davidson, Greathead and Green or Bacchus (which are usually signed) and also some French pieces which have their own odd look.
Other than that, there are other 'Etruscan' style pieces out there that are extremely hard to pin down. Like my three pieces
Sometimes I think that's because they were in vogue 1845 ish to 1860 so information is scarce or, like my blue vase and milchglas plate, they are so rare that it's hard to even find any criteria to match them on. And I'm fairly certain those of mine fall in to the 1840s/1850s, so that makes it quite difficult from a resource point of view.
There are some other pieces I see where I wonder if they were produced in a revival period of 'Etruscan' fashion from c.1880s or later and then I think you're blowing in the wind for a maker. There are a few styles that I see fairly often and wonder where on earth they've originated country wise.