It is possible to manually map the drive(s) to tape library using the registry value:
Key: HKLM -> Software -> Veeam -> Veeam Backup and Replication
Name: TapeDevices
Type: REG_MULTI_SZ
Data: TapeServer name (as shown in console)
Changer0=Tape0:ElementAddress
1. To get the proper data to be added into registry entry value we need to get the dump of Veeam Tape Remote Access Service:
For this please open on tape server Powershell as administrator and run there these commands:
>cd "C:\Program Files (x86)\Veeam\Backup Tape"
>.\VeeamTapeSvc.exe -dump
There will be created a file "dumpinformation.xml" in folder "C:\Program Files (x86)\Veeam\Backup Tape".
2. This is a basic XML tape service collects with all information about all tape devices. Open it with any XML editor (easiest way would be opening it in IE)
3. Navigate to the end of the XML and you will see a picture similar to this one:

4. The only thing left is to match tape DeviceName (Tape0, Tape1 etc.) with their ElementAddress values within the library.
So in this example scenario, the correct value for the registry entry will be the following (assuming tape server is shown in the console like this)
Key: HKLM -> Software -> Veeam -> Veeam Backup and Replication
Name: TapeDevices
Type: REG_MULTI_SZ
Data: VeeamTapeServer
Changer0=Tape1:0,Tape2:1