Backing up an encrypted external drive with Time Machine

I'm having a hard time understanding usage consequences of encryption of HDs with Time Machine. I encrypt my System HD with FileVault and have an external SSD I use for Time Machine. The TM drive is encrypted (option selected when I set it up as TM drive) - I do not keep it plugged in so enter that password each time I connect to do a backup, which is fine. I need to add a new external SSD and want to encrypt that as well - I believe I need to do that via Disk Utility as opposed to FileVault.

I have 2 requirements for this new external encrypted storage drive: 1) I don't want to have to manually enter it's password to access it at boot time or after waking from Sleep mode and 2) I want Time Machine to back this drive up along with the System HD, again without manually entering the pw for the new external drive.

When I do the encryption on the new external drive I get an option to save the password in Keychain. If I do this, will it meet both of my 2 requirements?

Also I do not normally use Keychain for anything (to my knowledge!) as I use 1Password as a password manager. Are there any problems with using Keychain to save this external hard drive password, while using 1Password for other passwords? I've on occasion had issues due to conflicts between 1Password and system password managers, but I don't know if this specific case of Keychain usage will cause such problems.

Thanks!

Bob