Managing SLA time count

Hello,

In short, we need to stop counting time towards SLA at night and weekends, for all non-critical tickets that remain open.

The only solution seems to be creating a new Status that doesn't count towards SLA, and manually set all non-critical open cases to this status by the end of each day, changing it back next morning.
This is not practical, but seems to be the only way. 'Operating Times' for our SLA must be set to 24/7 because we have a stand-by team that must respond to Critical cases that arise outside working hours, and resolution time must be accounted towards SLA.
An alternative would be to set two different 'Operating Times' on the same SLA, which is not possible on Sysaid, or to set two different SLA's for the same company with different 'Operating Times' each, which is also not possible on Sysaid, as far as I know.

If no better solution exists, I need help to create a new Status that doesn't count towards SLA.
When creating a new Status record, how can I set it to count or not to count? On Customize -> Lists -> Status there is no setting for this.
How can I tell which ticket Status count towards SLA anyway? I see that, for example, 'Pending for Others' status doesn't count, but can't find where to check / set this.

Thank you.