How to monitor a file share witness for accessibility

Question

In the context of a SQL Server Availability Group, what's the best way to monitor a file share witness for accessibility?

I want to make sure the witness can be accessed by the Availability Group replicas, which is something different than just being available. For instance, the account used to run SQL Server needs access rights to the file share.

Edit: I recently noticed some events logged by the cluster worthy of being monitored.

Log Name:      System
Source:        Microsoft-Windows-FailoverClustering
Date:          6/1/2019 1:23:09 PM
Event ID:      1564
Task Category: File Share Witness Resource
Level:         Critical
Keywords:     
User:          SYSTEM
Computer:      node1.contoso.com
Description:
File share witness resource 'File Share Witness' failed to arbitrate for
the file share '\\servername\sharename'. Please ensure that file share 
'\\servername\sharename' exists and is accessible by the cluster.

Log Name:      System
Source:        Microsoft-Windows-FailoverClustering
Date:          6/1/2019 1:23:08 PM
Event ID:      1562
Task Category: File Share Witness Resource
Level:         Warning
Keywords:     
User:          SYSTEM
Computer:      node1.contoso.com
Description:
File share witness resource 'File Share Witness' failed a periodic health
check on file share '\\servername\sharename'. Please ensure that file 
share '\\servername\sharename' exists and is accessible by the cluster.

Answer 1

The file share witness does not need to be accessible by the SQL Server service account. The FSW is used by the Windows Server Failover Clustering cluster to achieve a quorum and avoid split-brain scenarios. The cluster machine account is the AD principal that needs access to the FSW and if it did not have access you wouldn't be able to set it up as a witness in your cluster.

From an Availability Group perspective, it does not care about access to the FSW. The cluster cares about this and when it fails (and the quorum is lost) it signals the AG to shut down to avoid split-brain. The AG only cares about the SQL Server specific health checks (latency, connectivity to replicas etc) and the signals received from the WSFC cluster regarding cluster health.

If the cluster CNO loses rights to the FSW share then that resource would go offline in the cluster. This won't necessarily trigger any action in the cluster but should log alerts and events in the Windows Event Log for which you can monitor.