The following queries can be run in SQL to find all the Root Paths for a specified EV server:

For Indexes Use:

USE EnterpriseVaultDirectory
SELECT irp.IndexRootPath Partition_Path, ce.ComputerName EV_Server
FROM IndexRootPathEntry irp
INNER JOIN IndexingServiceEntry ise
on irp.IndexServiceEntryId = ise.serviceEntryId
INNER JOIN ComputerEntry ce
on ise.ComputerEntryId = ce.ComputerEntryId
WHERE ce.ComputerNameAlternate = 'EV_Server_Host_Name'

For Vault Store Partitions use:

USE EnterpriseVaultDirectory
SELECT pe.PartitionRootPath Partition_Path, ce.ComputerName EV_Server
FROM PartitionEntry pe
INNER JOIN VaultStoreEntry ve
on pe.VaultStoreEntryId = ve.VaultStoreEntryId
INNER JOIN StorageServiceEntry se
on ve.StorageServiceEntryId = se.ServiceEntryId
INNER JOIN ComputerEntry ce
on se.ComputerEntryId = ce.ComputerEntryId
WHERE ce.ComputerNameAlternate = 'EV_Server_Host_Name'

For both queries, replace EV_Server_Host_Name with  the host name of the failed EV server