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Ok I figured this one out. I had to mock the function call as follows:

class MyMocks(pulumi.runtime.Mocks):
    def new_resource(self, args: pulumi.runtime.MockResourceArgs):
        return [args.name + "_id", args.inputs]

    def call(self, args: pulumi.runtime.MockCallArgs):
        if args.token == "aws:index/getCallerIdentity:getCallerIdentity":
            return {
                "accountId": "123456789",
                "arn": "myarn",
                "id": "myid",
                "userId": "achang3"
            }
        return {}