Questions for Economic Advisers

Harvard's Greg Mankiw, an economic adviser to Mitt Romney, notes on his blog that Berkeley's Christina Romer and David Romer are economic advisers to Barack Obama; Stanford's Michael Boskin is advising Rudy Giuliani; and Boston University's Larry Kotlikoff is advising Mike Gravel.

I'm interested in how this process works, since being an adviser to a presidential candidate is generally considered to be a sign of support for that candidate. (No one, to my knowledge, is an economic adviser to more than one candidate, and Mankiw himself talks about where he "stands".)

On the other hand, being an economic adviser to a presidential can't really be considered a sign of support for that candidate's economic policies, since the whole point of hiring an economic adviser in the first place is to develop those policies.

So how are these marriages made? Do prominent economists reach out to presidential campaigns offering their services to the candidate they like the best for non-economics-related reasons? Would you ever find a Republican economist advising a Democratic candidate, or vice versa? And what are the chances of a campaign's economic adviser getting a plum job at the Fed or Treasury or the Council of Economic Advisers should the candidate ultimately win the presidency?

Maybe Greg Mankiw or Brad DeLong can help me out.