Make cascading select child searchable

[Sasha Solig]

I found this post which showed how to make a single select searchable (similar to the system Priority field). I would like to implement similar functionality on the child of a cascading select control, however I can't see how to make this work.

Note that I tried the above solution for single select, which made the parent searchable, however in my use case, it's the child that has hundreds of options and which I need to be able to search. I tried variants based on the child field name/id but with no luck.