Can I actively control my visibility settings, as with every other IM client? Inability to control my own visibility makes Hangouts an absolute non-starter for

Can I actively control my visibility settings, as with every other IM client? Inability to control my own visibility makes Hangouts an absolute non-starter for me, and many other people that I talk to. Our only choice is to keep it turned off at all times. Which is a shame, because Google Chat used to be my go-to messaging client.