This is just a short post as I stumbled over this in the past:
You want to define an action for a business partner object (Customer, Contact Person, Employee) but this is not possible because they are not ESF2 nodes - and only those support adding actions.
SAP provides the largely undocumented business object BusinessPartnerSolutionExtensions, which is ESF2. This business object is in sync with the default BusinessPartner business object - so for every UUID in BusinessPartner there's an identical UUID in BusinessPartnerSolutionExtensions.
So just create your action in BusinessPartnerSolutionExtensions and you will be able to link to the default BusinessParter using the UUID.