Having A Third Committee Member From A Different University - How To Pitch To The Third Member?
I suggest two things. First, most important, is that you don't make the pitch. Let one or both of your advisors do so, perhaps to a person you suggest. You might even give them a couple of suggestions and get their feedback.
It is harder to turn down an invitation from a peer than from an unknown student. The email, if that is the communication mechanism, will be read and likely not ignored.
Second make sure you lay out the responsibilities of the advisor early on so they are comfortable with the task they are taking on.