EventBridge target System Manager Automation pass in Execution Role

I defined a EventBridge Rule which targets a System Manager Automation I wrote. The Automation runs a Document that starts like:

schemaVersion: '0.3'
assumeRole: "{{ AutomationAssumeRole }}"
parameters:
  AutomationAssumeRole:
    type: String
    description: "(Required)"
    default: ""

For the EventBridge Rule, I define the Execution Role to be an IAM Role I created. I also configure an Input Transformer with some data about the event that triggered the Rule.

I want to pass in the Execution Role into the Automation's "AutomationAssumeRole" parameter.

If I manually trigger the Automation in the UI and select the Role from the dropdown, the Automation execution works as expected. I have not been able to figure out the right way to define the Input Transformer to have the EventBridge Rule trigger the Automation and populate the parameter "AutomationAssumeRole".