As we can see, Sixers, in the real world, are so hurriedly swaping their position to respawn in OASIS.
Why would they need to swap their position to respawn in OASIS?
TLDR
My answer is basically the same as @Rauv, but with a more detailed explanation as to why...
So this is never explained in the film and we there are no instances where this happens in the book to use as a comparison either. However, using other details from the book (and a real life comparison) we may be able to make an educated guess as to why the switch occurs. (I only have an audio book for this title so it would take some digging to get chapter sources...)
From the book and film we know that an OASIS account can be accessed from any OASIS console by simply logging into your online account. Once your retinal scan is verified and your passphrase/ password is entered you are returned to where your character last logged out of the system.
From the book we also know that when a user's avatar dies in the OASIS they see a replay of the last moments before their demise and then the dreaded prompt "GAME OVER." At that point their character is dead, they lose all of their stuff, and are returned to the process of creating a new character. Given what we were able to see from the film each time an IOI avatar was killed their rig went slack and the LEDs on the rig all swapped from white to red.
In addition we know from the book that your log in session can be force-ably cut. Should that happen your character is forced to remain stationary for (I believe) 60 seconds before the log out is initiated in the event you "rage quit" and it gives anyone or anything around you a chance to kill your avatar or whatever.
I mention all of this because using today's computers it is possible to perform the "switch user" action and rapidly change from one user to another. While there is no indication in either the book or the film that this function is available I personally see no reason why it would not exist. Given the economic status of the Ready Player One universe should a family only have one console to share with no consoles on loan from an online school, their job, etc. everyone in the family would use the same console to access the OASIS. Just as swapping users on today's computers pauses all function (print jobs and etc) I would see an OASIS console having the same functionality.
Also, while it is not explicitly defined it would seem from the film that the moment your headset is fully removed your character begins an automated log out or suspend process. Should another operator put that headset on, in my opinion, the display should return to the log in screen awaiting the "new" user to verify their account.
Regarding your question, it is my opinion that after the prior operator removed their harness their account would be signed out or suspended, pausing all current functions (i.e. returning to the character creation screen) and returning the console to the log in screen. Once the new user straps in the console would begin to verify their retinal scan and log them in to their last location. This would save time from the previous user needing to go through the motions of creating a new character or disconnecting from the current dead user account so that one of the stand by accounts can be accessed.
Personally I imagined that these are IOI's best and fastest machines so they are swapping the others out to go respawn and start getting back to the challenge while their fresh guys/gals on standby take over the better machines to immediately hop into the fray. (Realistically its total BS for movie drama and I know it XD)