Engage With an Executive Search Firm

Act as an executive career advisor. I am a [CURRENT_LEVEL] professional looking to engage with executive search (headhunter) firms for senior roles in [INDUSTRY]. I have never worked with headhunters before. Advise me on: how executive search firms work and how they differ from contingency recruiters, how to get on their radar without cold calling, what to send them as an introduction, how to manage a search firm relationship over time, and the critical difference between being a 'candidate' and being a 'source' to a headhunter.