Keeping Options Open While Working

Opening this thread up for down the line when folks get back into jobs and the market gets hot. 

We've seen a lot of layoffs and headcount reductions as of late, and some of the advice I've read on here is to always be talking to headhunters, recruiters, and outside options. It's one thing to hit oncycle or start talking to small/MM PE shops. But for those who want to stay in banking, how are you supposed to navigate headhunters? The one I see on linkedin is Selby Jennings, but by the tier of the city of the postings these are tiny banks. Even if they covered BBs/EBs, are you supposed to just hit them up asking for options? Is there a privacy clause somewhere? I would like to move in a year or 1.5 to similar BB (hope market picks up), but not sure how to manage navigating other banks/talking to options constantly. Any advice on talking to IB (large bank) headhunters or navigating the lateral process would be greatly appreciated.