Wess33 regarding your questions:
Q: [...]should I manually export it to pfx and then import it into the personal store of the second server where it's missing[...]
A: You can do that if you want. Just import it to the personal store of the computer and restart the MSExchangeServiceHost service on the computer on which the certificate was imported.
Q: Also, should I run the script command on the server where the cert is missing?
A: For running the ExportAuthCertificatesAsPfx logic of the script, yes, that's required. For the renewal / import logic, no it's not required but recommended.
Q: My concern is the script releqse notes page indicates the syntax will be renewing the Auth certificate?
A: In the past that was how the script worked. However, we've made some adjustments to the script (see: https://github.com/microsoft/CSS-Exchange/pull/1658). So, if the auth certificate is valid and no subject to be renewed due to its lifetime, it will be exported and imported. However, if you want to do it manually, feel free to do so by using the ExportAuthCertificatesAsPfx logic.