interface RDM <> hashicorp-vault manage SSH key

The interface between RDM and hashicorp-vault is working fine for a user/pwd authentication on a linux machine but does not work for a SSH key authentication.
Successfull exemple with user/pwd auth :
1 - Create a key/value entry in my hashicorp-vault serveur such as {"my_account": "my_password"}
2 - Create an hashicorp-vault objet in RDM with the host pointing on my hashicorp-vault serveur
3 - Create an SSH-SHELL session in RDM. I configure this session to point to the vault object (hashicorp-vault type) created on step 2, Then, I browse the hashicorp-vault tree to choise the {"my_account": "my_password"} key-value
4 -Open the SSH-SHELL session in RDM. If the user my_account existe on the linux, it s working fine

Does not work exemple with ssh key auth :
1 - Create a key/value entry in my hashicorp-vault serveur such as {"my_account": "-----BEGIN PRIVATE KEY-----\n my_key \n-----END PRIVATE KEY----"}
2- Follow the same steps 2&3 as above, except on step 4 (copy the pub key in the right place).
Impossible to open a session using an SSH Key located on hashicorp-vault