Error Logs in Json or Alternative Strategies?

I’m attempting to convert logs to json format. I’ve been able to do this for regular logs with a custom log-format and I also removed the timestamp from rsyslog. I’ve read the docs, googled, searched on here, etc. but I’m not certain if it’s possible to do this for error logs such as SSL failures. What’s I’ve read so far suggests it isn’t possible to modify error logs, only separate them into a different log file.

Does anyone know how to put error logs in json format, or have you developed any simple work around strategies?

Thanks for your help.