Methods for automating SQL CU patching?
I would not go with SQL agent running Patch to upgrade sql server. During patching and/or after patching SQL server needs to be restarted along with a reboot of windows machine - depending on the files that are locked during patching.

Alternatives are described in my answer here : https://dba.stackexchange.com/a/105837/8783

Also, dbatools has Update-DbaInstance.ps1 that can perform installation of SQL Server Service Packs and Cumulative Updates on local and remote servers.