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?
Found HKEY_LOCAL_MACHINE\SOFTWARE\ESRI\ArcGISPro\Licensing\LICENSE_SERVER key, will give that a try.
There are two registry options to consider, one is per machine and the other is per user. Per user is looked at FIRST, then if not found the per machine version of the key is looked at. These keys are at :
HKEY_CURRENT_USER\SOFTWARE\ESRI\ArcGISPro\Licensing
HKEY_LOCAL_MACHINE\SOFTWARE\ESRI\ArcGISPro\Licensing
The value of the LICENSE_SERVER key looks like @my_ESRILIC;@MY_ESRILICBACKUP. Technically you can have a port number before the @ symbol, but in ArcGIS Pro this does not appear to be honored (unlike ArcMap where the port number is usually set between 27000 and 27009).
Of note, the @ symbol is added automatically by ArcGIS Pro when you edit the License Manager names (or BACKUP name). This means you may end up with @@MY_ESRILIC in the registry when entering the LICENSE_SERVER name via the ArcGIS Pro License Settings page.
When testing, recall that the connection test is done during ArcGIS Pro start-up, this means by the time you get to the Licensing screen the connection check is already completed. This means any changes made to the registry manually or via the ArcGIS Pro interface are not 'operational' until ArcGIS Pro is restarted.