In ArcGIS Desktop (a.k.a., ArcMap) you can setup a connection to a failover license server by using the ArcGIS Administrator application and setting the License Manager to: Port@MyPrimaryServer;Port@MyFailoverServer
Or you can set HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\ESRI\License10.8\LICENSE_SERVER key.
In ArcGIS Pro licensing screen they have an option to setup a 'Backup' license server, this does not appear to work. Any hints on proper formatting for entering the server name for the backup? Is there a registry key that could be used?