As a reader, is there anything I can do to advocate an author's backlist being made available digitally? There are several authors I love (such as Brian Jacques and Robin McKinley) who had some well-known books a decade or two before ebooks were a thing--and these books aren't available digitally. Who's best to talk to--authors, agents, editors, or publishers? Will my begging do any good?
The best person to talk to is the author. Generally the author controls any unexploited rights (which is what you're talking about.) If you and many others clamor for an ebook, the author is the one who can show the demand to a publisher, or see there's a enough market to publish themselves.
Even if the author is sadly dead (as in the case of Brian Jacques) there's generally a way to get in touch via the webpage.
Fire off an email!