Can I back up an external drive with Photos app using Time Machine?

In the System Settings Time Machine controls, there is an "Options" choice that allows you to exclude things in the backup. Here, I've chosen to exclude some external volumes:

But you can choose to remove n volume with the little minus sign at the bottom, and thus to not exclude it.

scrubrnmom wrote:

can you back up an external drive with photos on to the time machine back up

Yes, if you do it with Time Machine. I have 4 external drives being backed up by Time Machine. One has several Photos libraries on it.