in battle royales this scenario is probably common (being "3rd partied" is what they call it?) and afaik in 99% of scenarios the team/person sandwiched from behind is focused because those are free kills and then favour the newest opponent because the survivors of the initial 1v1 have to invest time and resources into healing back up
If you're fishing for the argument "The player who sees you has a higher chance of preparing to win the second 1v1" then I feel that's quite niche unless you look at gamemodes where time to kill is extremely low like ffa cs:go gamemodes or CoD so there's more variance with odds of a clutch flick headshot. And even there you're still favoured to win so I'd say it doesn't matter much
In TF2 I doubt it matters. I'd wait like a second so maybe they shoot each other investing more hp and ammo into the 1v1, then get an easy kill on whoever survives.
Or just shoot the guy in the back, then wm1 at the dude who saw you but has low ammo and hp now so you're still highly favoured. There's always the chance of someone magically clutching a 1v2, yes. But believe in yourself. Just don't miss 3 meatshots on the person not looking at you