How get time-machine to backup my external (it cannot be deleted in options)?

I use 2 large external SSD drives for resources- and want to back these files up using TM along with my other files.

By default the external drives are listed in the settings as files that WILL NOT be backed-up.

The drives are listed, but greyed out - and cannot (as far as I can tell) be deleted or removed from the list. And therefore are not backed-up.

Note - I have tried this on 2 computers in my network, both have same issue.

How can I backup these important files to TM?