Try adding $context.error.validationErrorString and $context.integrationErrorMessage to the logs for the stage.
I added a bunch of stuff to the Log Format section, like this:
{ "requestId":"$context.requestId", "ip": "$context.identity.sourceIp",
"requestTime":"$context.requestTime", "httpMethod":"$context.httpMethod",
"routeKey":"$context.routeKey", "status":"$context.status",
"protocol":"$context.protocol", "errorMessage":"$context.error.message",
"path":"$context.path",
"authorizerPrincipalId":"$context.authorizer.principalId",
"user":"$context.identity.user", "caller":"$context.identity.caller",
"validationErrorString":"$context.error.validationErrorString",
"errorResponseType":"$context.error.responseType",
"integrationErrorMessage":"$context.integrationErrorMessage",
"responseLength":"$context.responseLength" }
In early development this allowed me to see this type of error:
{
"requestId": "QDu0QiP3oANFPZv=",
"ip": "76.54.32.210",
"requestTime": "21/Jul/2020:21:37:31 +0000",
"httpMethod": "POST",
"routeKey": "$default",
"status": "500",
"protocol": "HTTP/1.1",
"integrationErrorMessage": "The IAM role configured on the integration
or API Gateway doesn't have permissions to call the integration.
Check the permissions and try again.",
"responseLength": "35"
}