Hi @marcodenardi, thanks for the reply. This is very strange behaviour that I have been unable to replicate.
Can you try running these command on the shell and see if the eye tracker starts working after shutting the lid:
net stop "Tobii Service"
net start "Tobii Service"
This should restart the Tobii SW thus avoid the need to reinstall as a workaround. Let me know how it goes. Best Wishes.