Working with headhunters as a VP/Principal

Good question, wondering the same

I've personally found once you're on their radar / outreach list, there's a natural cadence when opportunities arise.  I haven't really found a reason to catch up specifically unless there's new information on my side to share.

Do you actively reach out to recruiters you have not spoke to before to get on their radar? 

The only benefit is if your criteria evolves over time -- sector interest, location, target size, etc. This way the opportunities recruiters send to you will be actionable. That said, I find recruiters most effective when you can be fully honest and saying you are actively looking will likely yield better results than saying you are just dipping your toe in the water. Recruiters want candidates that are committed.

Worth emailing to get on their list, but I don't see any point in checking in that often if you're not looking - it kind of wastes their time for them to set up a call and you continually say you aren't looking yet but just are just saying hi. They don't need constant reminders that you exist, if you start looking you can get more proactive.

IMO the time is much better spent developing industry connections, you'll get a lot more out of it and you could even land a role before it goes to the HH.