Thank you all for the replies. Stevie, those links are just what I was looking for.
I fully agree with the above. I didn't want to post a bunch of detail, but my initial meeting with clients always entails identifying who the target audience will be, so the demographics can inform all aspects of design. In this particular case, I have reason to believe the client's site will see more mobile visitors than average. I also believe his desire for certain mobile-unfriendly elements comes not from his own research, but rather an outdated ideal of what a web site should be. For context, he was using an old version of IE, and had never heard of Firefox.