Let's start with intercome.
I highly recommend that you not use mobile applications without the need, since they do not provide full functionality. Therefore, we will dismantle desktop versions
Everything is very easy here
To start, move the cursor to the icon of your profile at the bottom
After that you will see a new window in which you need to select the position named Your account. Press on this position
Then you get to the next screen where you need to select the position notifications. Press on this position
Then you need to tick mark column like this
And don't forget to save changes
After that, you will receive notifications of new messages directly to your desktop, after your shift, simply turn off notifications.
Unfortunately, zendesk does not have a notification function on the desktop, at least I did not find it, so we'll have to download the mobile application :(((
App named "zendesk support" so you can easily find it
Login with your zendesk account, then go to settings, sorry for russian interface
Then press on notifications postion
And simply turn ON
Now the notification of new messages or tickets will come to the phone.
But still I recommend to you, once every half hour check both the intercom and the zendesk, since something can always break down