Search: Search "within" a movie or TV series

"... I would go to the Full Cast and Crew page ...."

But the OP specifically mentioned an example (from The Fifth Element) of a voice role that is not listed on the Full Cast and Crew page.  In that particular instance, the relevant information can be found on the FAQ page, as I noted in my reply above.

Nobody,

While that explains the example, it doesn't address the actual question/suggestion. Whether or not IMDb would add the feature, hitting ctrl-F then adding even a few of the letters of the target info is going to be just as easy. Adding a feature to do what you can already do with a PC might improve the app versions, maybe.

Either way, like in the example, it'd only be guesswork not knowing how they might credit her...by her name, as Korbin's mother, as Mother, as Mom, etc. It might just end up being quicker to just open full cast and look (then try trivia, FAQ, the message board [Korbin's mother's voice], etc.).

(The apparent reason why the Full Credits page does not list that
voice role is because there is no known proof of the actor's identity.
The identification is speculative.  That is why it is listed on the FAQ page
instead of the credits page.)

In that example case, there is an alternative way to quickly find
the desired information, by using a site-specific Google search:

https://www.google.com/search?tbs=li:1&q=site%3Aimdb.com+%22fifth+element%22+%22korben%27s+mothe...

The first result of that search is the FAQ page
where the desired information can be found.

(Looking closely at that Google search result, note that it
even provides a convenient "Jump to..." link which leads directly
to the relevant FAQ section about "who plays the voices ....")