BUR #24324 has been approved by @nonamethanks.
create alias baton_(conducting) -> conductor_baton
Originally being given the odd (instrument) qualifier, this tag was given the (conducting) qualifier about 2 years ago to align it with the object's wikipedia article. This would have made sense with the old search autofill, except for the fact this type of *baton* was the only one that was ever given a qualifier, besides baton (weapon). Additionally, Wikipedia is the only place that names it like this; everywhere else, be it a musically focused site or just an Amazon shop listing, refers to it as a "conductor baton" or a "conducting baton", with the former having the most Google search results.
With the current autofill bahavior, there's no reason to not use the baton's common name like we were already doing for the other batons. No need for a utility alias for the alternative name, either, as "conduct" already finds both, though I would be open to using "conducting baton" instead if people preferred.