Yes, definitely add a tag wiki and a tag wiki excerpt!
I can't imagine a situation where it would ever be preferable to have no description. Even if the description is not complete (as it might not be here), something is better than nothing. And people can continue to add on to the existing tag wiki in the future, as other common uses are observed.
The only real question is whether a tag with so many different meanings is useful at all. But that's already been covered by the linked discussion and seems tangential to what you're asking here. If we've decided to keep the tag in spite of its possible flaws, then creating a tag wiki explaining its menagerie of meanings is definitely the best way of coping with the situation.