Identfy invisible characters with tooltip?

Than You for integrating no-break space (U+00A0)!
I suppose it is located in the “Punctuation” section?
But the only chance to get it, is using the search function (entering each time the correct name in full)
Maybe You could add a Tooltip on mouseover to all – or at least all invisible – characters, to give us a chance for quick selection of the character we are looking for?