I feel like these "tips" are from some kind of weird subculture I've never been part of. I've used 3rd party recruiters for almost 20 years and negotiation is always pretty transparent. I want X (which is more than I am currently making) and the recruiter finds a good fit. Sometimes the role is well above what I asked for.

Unless it's a boutique startup, I'm going to get into the role and find out right-quick what the salary bands are anyway, so the gaming seems silly. If it is some startup, I already provided the benefits I was looking for (and tradeoff for salary I would accept), so it doesn't seem to matter much.