Hi Rob,
I'm stuck .. really appreciate you sharing what you know about getting it up and running!
I went to https://code.google.com/apis/console per the instructions on the query of the Appointment object where I set up an operation which will hold the Google Calendar Sync settings. That Google site redirected to https://console.developers.google.com/iam-admin/projects where I have this project set up (I've truncated the Project ID and Project number in the screen shot):

I'm guessing Google must have changed their terminology since AwareIM set this up, because I don't find the Secret in the Google interface, so I assumed the Project Number in the Google screen is what AwareIM needs ???. As you can see in my initial testing, I am using System Settings rather than syncing the calendar by user for now:

Next I published the BSV and populated the System Settings values with the Google Project ID and Google Project Number as shown in the screen shot above. Then when running the query on the Appointment object I clicked on the Sync icon. The browser opened this window:

And eventually this arrived on the screen: "Authorization reply didn't arrive".
Any insights you can provide, Ron, would be greatly appreciated! I'm sure it's something simple.