Yes! That was the problem. The Tag is part of our site’s Third Party Addons Group. So I need to add a Third Party Addons tag before the supertool-script tag can be accepted by the tagging interface.
This is exactly backwards — if the feature is tool intended to be a time saver. I have to add tags twice and in a specific order. This is RPN for tagging.
If instead, it automagically added the parent tag group when the child tag was selected, that would be a time saver. Or if the child tags showed in the selector when the Parent tag Group was entered, the interface would basically have hints. (And selecting the Child tag should, again, add the Parent group.)