Creating a rule to pull back values on a field that don't exist

How about using a pivot task to count the number of Executive contacts?  I have a similar rule when an account has 0 touches by the CSM. 

There is probably a better way to do it, but here's the approach I've taken in the past:
1) pull one data set that has all of the contacts and their contact level
2) do a pivot task to get the total number of executives per account (accounts that have no executives will not show in this table)
3) pull another dataset of all of your accounts
4) merge the pivoted dataset with the all accounts dataset and use the merged data to trigger the CTA (where count of executives = null).

Hope this helps (or that someone else steps in with a better way that I can learn from)

Go Pivot Task! 
This sounds like a great approach.  A slight variant would be to merge with the Account list first.  Then when you do the pivot you can default those with no contacts to zero.  

We use a pivot task to perform a similar action with contacts. We pivot the 'Contact Role' field and set the customers health measure based on the number of contacts they have identified in, for example, the Decision Maker role. Customers with no contacts with null values in that field are moved to red.