AWS API Gateway and DynamoDb Serialization Exception Response Codes - amazon-dynamodb

Question

This question resolves how to fix serializaion errors caused by a bad template, but if they are cause by input errors like a missing param, they are returned with a 200.
I'm trying to add a response template for errors using the CDK on an DynamoDb integration
read_integration_responses=[aws_apigateway.IntegrationResponse(
status_code="200",
response_templates= {"application/json":read_response_template}),
aws_apigateway.IntegrationResponse(status_code="400",
response_templates={"text/html": "Client Error"},
selection_pattern="400" )
])
The 200 works fine, but I get a 500 server error when I have an error. The logs are no help:
Fri Feb 10 21:37:37 UTC 2023 : Sending request to
https://dynamodb.us-east-1.amazonaws.com/?Action=Query Fri Feb 10
21:37:37 UTC 2023 : Received response. Status: 400, Integration
latency: 6 ms Fri Feb 10 21:37:37 UTC 2023 : Endpoint response
headers: {Server=Server, Date=Fri, 10 Feb 2023 21:37:37 GMT,
Content-Type=application/x-amz-json-1.0, Content-Length=60,
Connection=keep-alive,
x-amzn-RequestId=HB4E7S3FS0NIMM44OQRN6RPBEBVV4KQNSO5AEMVJF66Q9ASUAAJG,
x-amz-crc32=3948637019} Fri Feb 10 21:37:37 UTC 2023 : Endpoint
response body before transformations:
{"__type":"com.amazon.coral.service#SerializationException"} Fri Feb
10 21:37:37 UTC 2023 : Execution failed due to configuration error:
Output mapping refers to an invalid method response: 400 Fri Feb 10
21:37:37 UTC 2023 : Method completed with status: 500
Per the method documentation selection_pattern is a string that matches the response code.