In this case, it’s better to rotate the camera continuously using gaze point offset from the middle of the screen instead of using ExtendedView script.
Make sure to use a continuous curve that defines how fast you rotate depending on that offset. You may possibly add some dead zone to that curve in the middle of the screen so that the user can use gaze for interaction as well as camera rotation.
Here you can find a video for what it may look like (from a master thesis by Cara Storath)
(scroll down to MASTER THESIS: MAKING EXISTING COMPUTER GAMES ACCESSIBLE VIA EYE-TRACKING)