@dpapad did we have IDs for most buttons in the old MD Settings page?

Yes. In the past "display-options-select-mirroring" element controlled mirroring an external display.

This is breaking our existing tests so this is a P2. Video team can't test playback performance metrics on ChromeOS without this element having an ID. 

Spoke with stevenjb@. He told me that 

"Tests that want to set display settings should use an extension that uses the chrome.system.display API)
https://developer.chrome.com/apps/system_display
See chrome.system.display.setDisplayProperties"

So I'm gonna just use an extension to set this up instead of using Chromedriver. That means that the missing IDs aren't a problem for me.

Relying on specific UI, especially something as changeable as the button ids, is definitely a problem.

As a short term workaround, one could try to execute something like the following JS from the chrome://settings page, assuming chromedriver allows that:

chrome.system.display.getDisplayLayout(function(layouts) {
  if (layouts.length < 2)
    // ERROR
  chrome.system.display.setDisplayProperties({
    id: layouts[1].id,
    mirroringSourceId: layouts[0].id,
  });
});

An extension is a better approach, but we may need to whitelist it in _api_features.json (unless you can run your test in kiosk mode).