AWS Cloudformation - How to attach vpc link / NLB to method in api gateway?

Question

This has been such a pain in the backend to waste hours and still unable to get one line of AWS CloudFormation syntax clear.

If the AWS guys can write their documentation slightly better - just pay a little bit more attention to it - it would make like easier for the developers.

I am trying to use CloudFormation to deploy API Gateway with VPC Link and NLB. The Goal is to proxy pass all requests to the NLB:

  ApiProxyMethod: 
    Type: AWS::ApiGateway::Method
    Properties: 
      RestApiId: !Ref ApiGatewayRestApi
      ResourceId: !Ref ApiProxyResource
      # AuthorizationScopes: # https://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/aws-resource-apigateway-method.html#cfn-apigateway-method-authorizationscopes
      AuthorizationType: COGNITO_USER_POOLS
      AuthorizerId: !Ref ApiAuthorizer
      HttpMethod: ANY
      OperationName: "ProxyAllRequests"
      Integration: 
        ConnectionType: VPC_LINK
        ConnectionId: !Ref ApiGatewayVpcLink
        IntegrationHttpMethod: ANY
        PassthroughBehavior: String
        Type: "VPC_LINK" # Member must satisfy enum value set: [HTTP, AWS_PROXY, HTTP_PROXY, AWS] 
        Uri: "http://NLB-myapp-internal-beta-12345.elb.ap-northeast-1.amazonaws.com/{proxy}"

However, this fails and it complains about wrong Type value: Member must satisfy enum value set: [HTTP, AWS_PROXY, HTTP_PROXY, AWS]

Now, which one of them is for VPC_Link / NLB?

They could have listed these values in the documentation of AWS::ApiGateway::Method Integration, but they choose not to.