As often in RPG, Which game do you play, what did you agree in session zero regarding the level of secrecy and the level of PvP. The answer is very different in a Vampire the Mascarade with an agreement on lethal PvP than on D&D full cooperative game
is there anything interesting happening while the party is split ? A shopping trip, especially for common items and with no pressure can be managed by the player without any GM intervention. On the other hand, having a PC telling the Prince about another PC behaviour requires some privacy.
Here are some stuff I use, depending on the game/context
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Small paper notes given directly to a PC (or given to the GM when being a PC) pretty great, especially when when PC have their SAN drifting low and you want to give different informations to everyone
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Limit the one by one time, like once, 10 minutes per session because if each players takes 30 minutes alone, sometimes twice, you end-up having PC playing 2 hours over a 6h sesssion, it sucks for everyone.
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Same technique as before, but keep everyone at the table, so players are aware of what's happening it also help saving time, in narrating what happened.
Then for the non active player, I tend to the rule-book on the PC side of the table, so they can use this time to review their abilities no matter whether we talk about PBTA like moves, D&D like spells or Cyberpunk-like gear. It's also the moment where they can take a small break to grab a coffee/snack or go to the restroom