Time Machine: Backing up the local drive onto an external AND a partition of that external to another external
Sounds like you have an external SSD drive that is partitioned for Time Machine and a different partition for Photos and you want to backup the Photos partition to a second external drive. This really has nothing to do with Time Machine.
There's a variety of ways to deal with this scenario.  You can clone the Photos partition to the second external drive using Disk Utility (restore function), command line dd tool, or a 3rd party tool such as SuperDuper! or CarbonCopyCloner. Some of which depends on the version of macOS you are running as the 3rd party software may only support Catalina or Big Sur on their latest versions.
If this is something you need to regularly run as a backup, I would recommend the commercial software such as CarbonCopyCloner to make it point and click easy.
In Disk Utility, attach both external drives, select the 2nd external drive where you will be copying the Photos partition to and click on Restore and then select the Photos partition on the first drive.  This will effectively clone the partition.
If you wish to do it from the command line in Terminal you need to first determine the drives identification.  /dev/disk3/disk3s2, etc. Use the command diskutil list to list all the drives and volumes (partitions) and be absolutely sure you understand which disk is which and that you make zero typos or you could clone the wrong thing or worse clone in the wrong direction effectively wiping out your data.  This is very powerful, rather straightforward but it is very unforgiving if you make a tragic mistake.
sudo dd if=/dev/disk1/disk1s2 of=/dev/disk2/disk2s1 bs=100M

Assuming you have 3 disks attached, /dev/disk0 would be your macOS Macintosh HD drive and supporting volumes (partitions).  /dev/disk1 would be the first Time Machine drive with the Photos volume (partition). The photos partition is likely the second partition /dev/disk1/disk1s2. The destination is /dev/disk2/disk2s1 creating a clone of /dev/disk1/disk1s2 on the first partition on the second disk /dev/disk2/disk2s1.

This is ONLY AN EXAMPLE, you need to determine what the correct disk identifiers are for your particular setup as they will likely vary.
For the technical people, cloning a drive from the command line for free allows for scripting and a DIY attitude.  But using software such as CarbonCopyCloner is far easier, less error prone, and worth every penny if you do this all the time. The latest version of CCC was recently updated and one of the main features was increased performance with a new multi-threaded file-copier. It may be a better choice over Time Machine as well. Depends on your particular needs.