Being an Account Manager, he should be able to track the following,

           Check all the new tickets created under his Account.

           

           Track the changes made to the existing tickets by other technicians/Users.

Since there is no option to notify the Account Manager separately using Notification Rule , the same can be achieved using Custom Trigger with some specific Criteria,

Create a Custom Trigger with a specific criteria like Sender is ( mention the requester's email id ) or you can configure an additional field in the Incident Template and pre configure a value for that field .Associate the specific Account ( to which the Account Manager  is part of ) to the Custom Trigger. Set the Execute option as "When a request is created and edited". Set the criteria as the additional field specified in the incident template.

Now when users from that Account create a new ticket using the incident template will meet the criteria and the Custom Trigger will get executed.

Download the attached index.bat and SendEmail.exe and place it in the path ServiceDeskPlus-MSP\integration\custom_scripts

Refer the attached image (SendEmail.png) on how to configure the Custom Trigger. 

The index.bat file will have the entries like below,

sendemail.exe -f emailid -t xyz@domain.com -u "test" -m "test2" -s sdpmsplinmail.com:25

In the above syntax,

Now if any user in that Account raise a new ticket or edit an existing ticket with the respective criteria met, then the Account Manager will get notified by Email.