The Package Service is installed on the SMP. It seemed to be running correctly but it was not publishing HTTPS codebases. The respective HTTPS codebases settings have been enabled as per the following article:
Note: This can also occur on another Site Server and not just for the SMP Server itself running the Package Service.
ITMS 8.x
When running both the SMP and Site Server on the same host you can't override the certificate used on the Site Server. This issue is that you'd have two web servers binding to port 443 using two different certificates. This is why it failed.
In the case of a separate Site Server, this issue can be caused by an outdated Site Server certificate or a different Server CA certificate used in the past for the Site Server.