text: I'm curious for a real-world example of a lift gate where 'foot' isn't allowed. The signs usually refer to a road or area, not the barrier. It hasn't even been properly discussed whether access tags on barriers are about passing the barrier or operation of the barrier. E.g. access=private may also mean that only authorized people are allowed to open and close a lift gate, while everbody is allowed to pass it when possible.
  
  To answer your question about the proper tags: For the specific case the note is about, you can use the width tags I mentioned. In general, I think that we need a new tag such as locked=no/padlock/electric/wire/permanent together with operation=manual/switch/key/automatic/remote/smart_card/fingerprint, similar in spirit (but not in syntax) to https://wiki.openstreetmap.org/wiki/Proposed_features/entrance/door#Accessibility_information. These tags can not only be used on barriers, but also on buildings, hunting stands, boxes, and anything that can be opened and closed. I have been comtemplating for ages to write a proposal... I'll support you if you do it. :-)