Video drivers have been updated, but that doesn't appear to have solved the issue.
I rebooted the secondary, but when I connected via multiplicity I still got the black screen. After logging in with RDP and connecting to the machine with multiplicity while RDP was still open, I would get to the login screen and multiplicity would work as expected.
After idling with multiplicity for a while, multiplicity gave me a message about having lost it's connection. I could see what was happening on the secondary, but could not interact with anything.
Windows firewall is off on both machines, so I don't believe that is part of the issue. Both machines are on the same subnet at the router, and there doesn't appear to be any issue that would prevent them from connecting at the router/switch level. Ping works fine to the secondary when I'm getting the black screen issue and RDP works all the time as well.