New member event for Business Rules

I was hoping to be able to resolve this by creating an event of "After updating entity" but when I select "Group relationship" for Target Entity Type, the target bundle doesn't populate with values for for example "groupname-group_membership" in the dropdown. I was thinking there is a path to create rules to handle actions after new member is joined or leaves but can't even get past creation of BR reacts on event to test.

I'm interested in this as well. In my case I want to give specific group roles to users with specific site roles.

Moving to the Business Rules issue queue. Not sure what I can do here.