mediaconvert error 1404

Is the source file located in an S3 bucket of the same AWS account as the MediaConvert job being run? If not, the bucket policy would need to allow cross account access. You may want to reconfirm that the selected MediaConvert IAM role for the job includes S3 full access. The error may indicate that the MP4 file is corrupt, or that MediaConvert is unable to read the metadata from the file header. See if the file can be played without error. If you have a tool to extract the file metadata, validate that the data is fully available.

Being in Gov-Cloud could have some restrictions. I'll need to check on that.

For metadata extraction you could use MediaInfo or perhaps FF-MPEG, either of which could be run in an AWS Lambda function. You may want to search for other freeware tools that my provide the metadata in a web UI application (instead of running AWS services).

The 1404 error is an S3 response. MediaConvert is unable to load the file. That could mean that access permissions to the file is not working.

Do other files from the same S3 bucket have the same error?

You may want to submit an AWS Support ticket, providing account ID, MediaConvert job ID and region. AWS Elemental Support could then retrieve the logs to better determine what was the interaction between MediaConvert and S3.