I wouldn't say that it would "see-saw" but you could adjust its angle slightly when tightened. It takes a couple of muscles to move it once mounted, but not a lot of muscle. Bumping it with your head might shift it a small amount, but nothing catastrophic and maybe 1/16 to 1/8 of an inch depending on how big of a bump you have on your head. LOL

Farewell - June 4, 2020