Time Machine: backing up 2 drives at once

[Sarcany]

Weird.

Are both drives called "Macintosh HD" ...? There might be a conflict.

Maybe rename the external boot drive to "Macintosh SSD" and then let it back up once so that it updates the backup properly with the name-change and then reboot and see if the internal drive shows up in the exclude list.

(Just throwing stuff at the fan..)