Same issue w/ wildcard as the CN and added detail of being an external cert. External cert FQDN is different from local AD domain. Thus cert is *.externaldomain.com, FQDN is box.externaldomain.com while FQDN for server PC is box.internaldomain.local. (Use of CName in the DNS directs the external FQDN to local FQDN. Utilize WebContextURL property on Server to facilitate.)
Did the client PC step above. No fix.
Fiddler shows initially hitting the external FQDN via the HTTP port 443, then querying for download.esri.com, then esrisoftware.esri.com, then it queries for the local AD domain FQDN and fails.
Workaround is to set AGOL portal as the active, but would like to fix if possible.